Daily Papers

This paper puts forward an integrated microstructure design methodology that replaces the common existing design approaches: 1) reconstruction of microstructures, 2) analyzing and quantifying material properties, and 3) inverse design of materials using deep-learned generative and surrogate models. The long-standing issue of microstructure reconstruction is well addressed in this study using a new class of state-of-the-art generative model, the diffusion-based generative model (DGM). Moreover, the conditional formulation of DGM for guidance to the embedded desired material properties with a transformer-based attention mechanism enables the inverse design of multifunctional composites. A convolutional neural network (CNN)-based surrogate model is utilized to analyze the nonlinear material behavior to facilitate the prediction of material properties for building microstructure-property linkages. Combined, these generative and surrogate models enable large data processing and database construction that is often not affordable with resource-intensive finite element method (FEM)-based direct numerical simulation (DNS) and iterative reconstruction methods. An example case is presented to demonstrate the effectiveness of the proposed approach, which is designing mechanoluminescence (ML) particulate composites made of europium and dysprosium ions. The results show that the inversely-designed multiple ML microstructure candidates with the proposed generative and surrogate models meet the multiple design requirements (e.g., volume fraction, elastic constant, and light sensitivity). The evaluation of the generated samples' quality and the surrogate models' performance using appropriate metrics are also included. This assessment demonstrates that the proposed integrated methodology offers an end-to-end solution for practical material design applications.

The ability to generate 3D multiphase microstructures on-demand with targeted attributes can greatly accelerate the design of advanced materials. Here, we present a conditional latent diffusion model (LDM) framework that rapidly synthesizes high-fidelity 3D multiphase microstructures tailored to user specifications. Using this approach, we generate diverse two-phase and three-phase microstructures at high resolution (volumes of 128 times 128 times 64 voxels, representing >10^6 voxels each) within seconds, overcoming the scalability and time limitations of traditional simulation-based methods. Key design features, such as desired volume fractions and tortuosities, are incorporated as controllable inputs to guide the generative process, ensuring that the output structures meet prescribed statistical and topological targets. Moreover, the framework predicts corresponding manufacturing (processing) parameters for each generated microstructure, helping to bridge the gap between digital microstructure design and experimental fabrication. While demonstrated on organic photovoltaic (OPV) active-layer morphologies, the flexible architecture of our approach makes it readily adaptable to other material systems and microstructure datasets. By combining computational efficiency, adaptability, and experimental relevance, this framework addresses major limitations of existing methods and offers a powerful tool for accelerated materials discovery.

Decentralized prediction markets (DePMs) allow open participation in event-based wagering without fully relying on centralized intermediaries. We review the history of DePMs which date back to 2011 and includes hundreds of proposals. Perhaps surprising, modern DePMs like Polymarket deviate materially from earlier designs like Truthcoin and Augur v1. We use our review to present a modular workflow comprising eight stages: underlying infrastructure, market topic, share structure and pricing, market initialization, trading, market resolution, settlement, and archiving. For each module, we enumerate the design variants, analyzing trade-offs around decentralization, expressiveness, and manipulation resistance. We also identify open problems for researchers interested in this ecosystem.

We develop a rigorous walk-forward validation framework for algorithmic trading designed to mitigate overfitting and lookahead bias. Our methodology combines interpretable hypothesis-driven signal generation with reinforcement learning and strict out-of-sample testing. The framework enforces strict information set discipline, employs rolling window validation across 34 independent test periods, maintains complete interpretability through natural language hypothesis explanations, and incorporates realistic transaction costs and position constraints. Validating five market microstructure patterns across 100 US equities from 2015 to 2024, the system yields modest annualized returns (0.55%, Sharpe ratio 0.33) with exceptional downside protection (maximum drawdown -2.76%) and market-neutral characteristics (beta = 0.058). Performance exhibits strong regime dependence, generating positive returns during high-volatility periods (0.60% quarterly, 2020-2024) while underperforming in stable markets (-0.16%, 2015-2019). We report statistically insignificant aggregate results (p-value 0.34) to demonstrate a reproducible, honest validation protocol that prioritizes interpretability and extends naturally to advanced hypothesis generators, including large language models. The key empirical finding reveals that daily OHLCV-based microstructure signals require elevated information arrival and trading activity to function effectively. The framework provides complete mathematical specifications and open-source implementation, establishing a template for rigorous trading system evaluation that addresses the reproducibility crisis in quantitative finance research. For researchers, practitioners, and regulators, this work demonstrates that interpretable algorithmic trading strategies can be rigorously validated without sacrificing transparency or regulatory compliance.

The diffusion MRI Neurite Exchange Imaging model offers a promising framework for probing gray matter microstructure by estimating parameters such as compartment sizes, diffusivities, and inter-compartmental water exchange time. However, existing protocols require long scan times. This study proposes a reduced acquisition scheme for the Connectome 2.0 scanner that preserves model accuracy while substantially shortening scan duration. We developed a data-driven framework using explainable artificial intelligence with a guided recursive feature elimination strategy to identify an optimal 8-feature subset from a 15-feature protocol. The performance of this optimized protocol was validated in vivo and benchmarked against the full acquisition and alternative reduction strategies. Parameter accuracy, preservation of anatomical contrast, and test-retest reproducibility were assessed. The reduced protocol yielded parameter estimates and cortical maps comparable to the full protocol, with low estimation errors in synthetic data and minimal impact on test-retest variability. Compared to theory-driven and heuristic reduction schemes, the optimized protocol demonstrated superior robustness, reducing the deviation in water exchange time estimates by over two-fold. In conclusion, this hybrid optimization framework enables viable imaging of neurite exchange in 14 minutes without loss of parameter fidelity. This approach supports the broader application of exchange-sensitive diffusion magnetic resonance imaging in neuroscience and clinical research, and offers a generalizable method for designing efficient acquisition protocols in biophysical parameter mapping.

Paper 1 of this research programme develops a resolution-aware risk-design framework for the simplest event-linked perpetual: a contract whose underlying tracks a single binary prediction-market probability through resolution. The instrument class is broader. Variants span conditional probabilities P(A|B), spreads p^A - p^B, weighted baskets sum w_i p^(i), derivatives on variance or entropy of the probability process, contracts on liquidity itself, perpetual-on-expiring-event roll structures, and funding-only derivatives with no settlement. Each variant inherits some framework components from the single-market binary case and requires its own design adaptations. This paper develops a formal taxonomy of seven pure-form canonical variants beyond the probability-index perpetual of Paper 1, organised along four orthogonal design axes: underlying geometry, temporal structure, settlement structure, and venue composition. The list is not exhaustive; combinations are not treated separately. For each variant we provide a precise payoff definition; an inheritance map identifying which Paper 1 components carry over, are modified, or fail; variant-specific design constraints; microstructure properties; empirical evaluability on the PMXT v2 archive; and limitations. Notable findings: the conditional variant admits a candidate non-portability proposition (denominator instability as the conditioning event becomes improbable); the spread variant requires a three-channel decomposition of resolution risk; the volatility/entropy variant avoids random binary terminal-collapse but introduces estimator-convention and entropy-decay issues; the basket variant requires multi-period jump-aware margin whose aggregation is correlation-dependent. The paper is theoretical primarily; it specifies how demonstrative time series can be constructed and provides evaluability criteria to guide future work.

Materials characterization is fundamental to acquiring materials information, revealing the processing-microstructure-property relationships that guide material design and optimization. While multimodal large language models (MLLMs) have recently shown promise in generative and predictive tasks within materials science, their capacity to understand real-world characterization imaging data remains underexplored. To bridge this gap, we present MatCha, the first benchmark for materials characterization image understanding, comprising 1,500 questions that demand expert-level ___domain expertise. MatCha encompasses four key stages of materials research comprising 21 distinct tasks, each designed to reflect authentic challenges faced by materials scientists. Our evaluation of state-of-the-art MLLMs on MatCha reveals a significant performance gap compared to human experts. These models exhibit degradation when addressing questions requiring higher-level expertise and sophisticated visual perception. Simple few-shot and chain-of-thought prompting struggle to alleviate these limitations. These findings highlight that existing MLLMs still exhibit limited adaptability to real-world materials characterization scenarios. We hope MatCha will facilitate future research in areas such as new material discovery and autonomous scientific agents. MatCha is available at https://github.com/FreedomIntelligence/MatCha.

In quality control, microstructures are investigated rigorously to ensure structural integrity, exclude the presence of critical volume defects, and validate the formation of the target microstructure. For quenched, hierarchically-structured steels, the morphology of the bainitic and martensitic microstructures are of major concern to guarantee the reliability of the material under service conditions. Therefore, industries conduct small sample-size inspections of materials cross-sections through metallographers to validate the needle morphology of such microstructures. We demonstrate round-robin test results revealing that this visual grading is afflicted by pronounced subjectivity despite the thorough training of personnel. Instead, we propose a deep learning image classification approach that distinguishes steels based on their microstructure type and classifies their needle length alluding to the ISO 643 grain size assessment standard. This classification approach facilitates the reliable, objective, and automated classification of hierarchically structured steels. Specifically, an accuracy of 96% and roughly 91% is attained for the distinction of martensite/bainite subtypes and needle length, respectively. This is achieved on an image dataset that contains significant variance and labeling noise as it is acquired over more than ten years from multiple plants, alloys, etchant applications, and light optical microscopes by many metallographers (raters). Interpretability analysis gives insights into the decision-making of these models and allows for estimating their generalization capability.

Statistics of grain sizes and orientations in metals correlate to the material's mechanical properties. Reproducing representative volume elements for further analysis of deformation and failure in metals, like 316L stainless steel, is particularly important due to their wide use in manufacturing goods today. Two approaches, initially created for video games, were considered for the procedural generation of representative grain microstructures. The first is the Wave Function Collapse (WFC) algorithm, and the second is constraint propagation and probabilistic inference through Markov Junior, a free and open-source software. This study aimed to investigate these two algorithms' effectiveness in using reference electron backscatter diffraction (EBSD) maps and recreating a statistically similar one that could be used in further research. It utilized two stainless steel EBSD maps as references to test both algorithms. First, the WFC algorithm was too constricting and, thus, incapable of producing images that resembled EBSDs. The second, MarkovJunior, was much more effective in creating a Voronoi tessellation that could be used to create an EBSD map in Python. When comparing the results between the reference and the generated EBSD, we discovered that the orientation and volume fractions were extremely similar. With the study, it was concluded that MarkovJunior is an effective machine learning tool that can reproduce representative grain microstructures.

The advancement of Large Language Models (LLMs) for ___domain applications in fields such as materials science and engineering depends on the development of fine-tuning strategies that adapt models for specialized, technical capabilities. In this work, we explore the effects of Continued Pretraining (CPT), Supervised Fine-Tuning (SFT), and various preference-based optimization approaches, including Direct Preference Optimization (DPO) and Odds Ratio Preference Optimization (ORPO), on fine-tuned LLM performance. Our analysis shows how these strategies influence model outcomes and reveals that the merging of multiple fine-tuned models can lead to the emergence of capabilities that surpass the individual contributions of the parent models. We find that model merging leads to new functionalities that neither parent model could achieve alone, leading to improved performance in ___domain-specific assessments. Experiments with different model architectures are presented, including Llama 3.1 8B and Mistral 7B models, where similar behaviors are observed. Exploring whether the results hold also for much smaller models, we use a tiny LLM with 1.7 billion parameters and show that very small LLMs do not necessarily feature emergent capabilities under model merging, suggesting that model scaling may be a key component. In open-ended yet consistent chat conversations between a human and AI models, our assessment reveals detailed insights into how different model variants perform and show that the smallest model achieves a high intelligence score across key criteria including reasoning depth, creativity, clarity, and quantitative precision. Other experiments include the development of image generation prompts based on disparate biological material design concepts, to create new microstructures, architectural concepts, and urban design based on biological materials-inspired construction principles.

The design of functional materials with desired properties is essential in driving technological advances in areas like energy storage, catalysis, and carbon capture. Generative models provide a new paradigm for materials design by directly generating entirely novel materials given desired property constraints. Despite recent progress, current generative models have low success rate in proposing stable crystals, or can only satisfy a very limited set of property constraints. Here, we present MatterGen, a model that generates stable, diverse inorganic materials across the periodic table and can further be fine-tuned to steer the generation towards a broad range of property constraints. To enable this, we introduce a new diffusion-based generative process that produces crystalline structures by gradually refining atom types, coordinates, and the periodic lattice. We further introduce adapter modules to enable fine-tuning towards any given property constraints with a labeled dataset. Compared to prior generative models, structures produced by MatterGen are more than twice as likely to be novel and stable, and more than 15 times closer to the local energy minimum. After fine-tuning, MatterGen successfully generates stable, novel materials with desired chemistry, symmetry, as well as mechanical, electronic and magnetic properties. Finally, we demonstrate multi-property materials design capabilities by proposing structures that have both high magnetic density and a chemical composition with low supply-chain risk. We believe that the quality of generated materials and the breadth of MatterGen's capabilities represent a major advancement towards creating a universal generative model for materials design.

Data-driven surrogate models are an alternative to numerical homogenization of heterogeneous materials. In this contribution, a supervised learning approach is presented for predicting effective Lamé parameters of hyperelastic composites from low-dimensional microstructural descriptors. The data set is based on previously published numerical homogenization results for ensembles of two-phase stochastic microstructures generated by planar Boolean models, covering variations of inclusion shape, phase contrast, and area fraction; see Brändel, Brands, Maike, Rheinbach, Schröder, Schwarz and Stoyan (2022). A neural network is trained on combinations of scalar and curve-valued statistical descriptors, including the area fraction, a derived scalar shape descriptor τ, the two-point correlation function S_2(r), and the lineal-path function ell(z). Additional data representing limiting cases of the parameter space are incorporated to stabilize training and improve extrapolation behavior. The surrogate is evaluated by leave-one-grain-type-out cross-validation in order to assess generalization to unseen grain geometries. Numerical results demonstrate that additional descriptors can reduce relative errors. A predictor trained with τ and S_2(r) provides a compact representation with good quantitative accuracy and regular dense response behavior. Adding the lineal-path function ell(z) further reduces the error at the available data points, indicating that it is a promising additional descriptor; however, dense post-training response evaluations show that improved pointwise accuracy does not automatically guarantee physically admissible behavior between sampled parameter values. This motivates future work on physically constrained surrogate models, loss formulations, bounded output parametrizations, and a more systematic representation of curve-valued geometric descriptors.

We apply preference learning to the task of language model-guided design of novel structural alloys. In contrast to prior work that focuses on generating stable inorganic crystals, our approach targets the synthesizeability of a specific structural class: BCC/B2 superalloys, an underexplored family of materials with potential applications in extreme environments. Using three open-weight models (LLaMA-3.1, Gemma-2, and OLMo-2), we demonstrate that language models can be optimized for multiple design objectives using a single, unified reward signal through Direct Preference Optimization (DPO). Unlike prior approaches that rely on heuristic or human-in-the-loop feedback (costly), our reward signal is derived from thermodynamic phase calculations, offering a scientifically grounded criterion for model tuning. To our knowledge, this is the first demonstration of preference-tuning a language model using physics-grounded feedback for structural alloy design. The resulting framework is general and extensible, providing a path forward for intelligent design-space exploration across a range of physical science domains.

Accelerated materials discovery is an urgent demand to drive advancements in fields such as energy conversion, storage, and catalysis. Property-directed generative design has emerged as a transformative approach for rapidly discovering new functional inorganic materials with multiple desired properties within vast and complex search spaces. However, this approach faces two primary challenges: data scarcity for functional properties and the multi-objective optimization required to balance competing tasks. Here, we present a multi-property-directed generative framework designed to overcome these limitations and enhance site symmetry-compliant crystal generation beyond P1 (translational) symmetry. By incorporating Wyckoff-position-based data augmentation and transfer learning, our framework effectively handles sparse and small functional datasets, enabling the generation of new stable materials simultaneously conditioned on targeted space group, band gap, and formation energy. Using this approach, we identified previously unknown thermodynamically and lattice-dynamically stable semiconductors in tetragonal, trigonal, and cubic systems, with bandgaps ranging from 0.13 to 2.20 eV, as validated by density functional theory (DFT) calculations. Additionally, we assessed their thermoelectric descriptors using DFT, indicating their potential suitability for thermoelectric applications. We believe our integrated framework represents a significant step forward in generative design of inorganic materials.

Latent heat thermal energy storage (LHTES) systems are compelling candidates for energy storage, primarily owing to their high storage density. Improving their performance is crucial for developing the next-generation efficient and cost effective devices. Topology optimization (TO) has emerged as a powerful computational tool to design LHTES systems by optimally distributing a high-conductivity material (HCM) and a phase change material (PCM). However, conventional TO typically limits to optimizing the geometry for a fixed, pre-selected materials. This approach does not leverage the large and expanding databases of novel materials. Consequently, the co-design of material and geometry for LHTES remains a challenge and unexplored. To address this limitation, we present an automated design framework for the concurrent optimization of material choice and topology. A key challenge is the discrete nature of material selection, which is incompatible with the gradient-based methods used for TO. We overcome this by using a data-driven variational autoencoder (VAE) to project discrete material databases for both the HCM and PCM onto continuous and differentiable latent spaces. These continuous material representations are integrated into an end-to-end differentiable, transient nonlinear finite-element solver that accounts for phase change. We demonstrate this framework on a problem aimed at maximizing the discharged energy within a specified time, subject to cost constraints. The effectiveness of the proposed method is validated through several illustrative examples.

Material selection plays a pivotal role in many industries, from manufacturing to construction. Material selection is usually carried out after several cycles of conceptual design, during which designers iteratively refine the design solution and the intended manufacturing approach. In design research, material selection is typically treated as an optimization problem with a single correct answer. Moreover, it is also often restricted to specific types of objects or design functions, which can make the selection process computationally expensive and time-consuming. In this paper, we introduce MSEval, a novel dataset which is comprised of expert material evaluations across a variety of design briefs and criteria. This data is designed to serve as a benchmark to facilitate the evaluation and modification of machine learning models in the context of material selection for conceptual design.

Inverse materials design starts from target functionality and searches for structures that can realize it. Its value in closed-loop discovery depends not only on prediction performance, but also on whether expensive first-principles results are independently validated, provenance-recorded, and admitted as feedback only when evidence is sufficient. This is especially important for composite properties such as carrier mobility, where a final scalar value hides intermediate quantities, fit quality, convergence history, and workflow assumptions. Here we present InvDesMobility, a reliability-gated first-principles feedback framework that integrates multi-agent automated DFT, evidence stratification, generative structure proposal, acquisition ranking, and auditable release. Using 516 2DMatPedia-derived candidates, the workflow produced 280 QC-passed materials and 573 retained carrier-direction seed channels after channel-level reliability gating. These records were split into two feedback objects: relaxed structures updated the generative model, while retained mobility channels trained the acquisition model and set validation priority. Over multiple iterations, InvDesMobility screened 2.4 x 10^6 structures, submitted 102 candidates for DFT validation, and retained 86 reliability-gated generated channels across 41 formulas. Overall, the main contribution is not a fixed list of high-mobility materials, but a transferable feedback contract that makes closed-loop inverse design both useful and auditable when learning from expensive calculated properties. All source data, retained feedback records, and workflows are available at https://github.com/DreamLufei/invDesMobility, with an accompanying evidence website at https://dreamlufei.github.io/invDesMobility/.

We present a generative framework for inverse design of five-layer transmissive Huygens' metasurfaces (HMSs), addressing a longstanding challenge in achieving full-phase, high-efficiency unit cell designs with minimal full-wave simulations. The key to achieving this is our reliance on the field-based semianalytical (SA) scheme developed in Part I of this paper, which allows rapid and highly effective synthesis of such multilayer composites, however with limited accuracy. To overcome the prohibitive data demands of traditional pipelines, we employ Mamba, a selective state space model well suited for long-range sequence modeling as the backbone of our learning framework. A bidirectional Mamba (Bi-Mamba) forward surrogate is first trained on SA-generated data and subsequently fine-tuned with full-wave CST samples. An ablation over a 1080-sample CST pool shows that as few as 270 full-wave calibration samples suffice to reach near-CST-level agreement at a fraction of the simulation cost. An autoregressive Mamba inverse generator is subsequently trained on surrogate-augmented data, treating unit-cell synthesis as a sequential generation task. The resulting one-to-many generative model produces diverse unit cell geometries conditioned on target scattering responses. It achieves CST-validated designs with field transmission magnitude 0.9 across the full 0-2π phase range at 20 GHz. Moreover, a CST-calibrated surrogate trained to accurately predict frequency responses (18-22 GHz) enables functional post-selection of inverse generated designs. Together, the hybrid SA-generative methodology in this two-part compilation establishes a scalable and data-efficient solution for multilayer HMS synthesis, with natural extensions toward broadband, oblique-incidence, and higher-dimensional electromagnetic inverse-design problems.

Generative models have had a profound impact on vision and language, paving the way for a new era of multimodal generative applications. While these successes have inspired researchers to explore using generative models in science and engineering to accelerate the design process and reduce the reliance on iterative optimization, challenges remain. Specifically, engineering optimization methods based on physics still outperform generative models when dealing with constrained environments where data is scarce and precision is paramount. To address these challenges, we introduce Diffusion Optimization Models (DOM) and Trajectory Alignment (TA), a learning framework that demonstrates the efficacy of aligning the sampling trajectory of diffusion models with the optimization trajectory derived from traditional physics-based methods. This alignment ensures that the sampling process remains grounded in the underlying physical principles. Our method allows for generating feasible and high-performance designs in as few as two steps without the need for expensive preprocessing, external surrogate models, or additional labeled data. We apply our framework to structural topology optimization, a fundamental problem in mechanical design, evaluating its performance on in- and out-of-distribution configurations. Our results demonstrate that TA outperforms state-of-the-art deep generative models on in-distribution configurations and halves the inference computational cost. When coupled with a few steps of optimization, it also improves manufacturability for out-of-distribution conditions. By significantly improving performance and inference efficiency, DOM enables us to generate high-quality designs in just a few steps and guide them toward regions of high performance and manufacturability, paving the way for the widespread application of generative models in large-scale data-driven design.

The discovery of novel mechanical metamaterials, whose properties are dominated by their engineered structures rather than chemical composition, is a knowledge-intensive and resource-demanding process. To accelerate the design of novel metamaterials, we present MetaScientist, a human-in-the-loop system that integrates advanced AI capabilities with expert oversight with two primary phases: (1) hypothesis generation, where the system performs complex reasoning to generate novel and scientifically sound hypotheses, supported with ___domain-specific foundation models and inductive biases retrieved from existing literature; (2) 3D structure synthesis, where a 3D structure is synthesized with a novel 3D diffusion model based on the textual hypothesis and refined it with a LLM-based refinement model to achieve better structure properties. At each phase, ___domain experts iteratively validate the system outputs, and provide feedback and supplementary materials to ensure the alignment of the outputs with scientific principles and human preferences. Through extensive evaluation from human scientists, MetaScientist is able to deliver novel and valid mechanical metamaterial designs that have the potential to be highly impactful in the metamaterial field.

Metasurfaces are ultrathin, engineered materials composed of nanostructures that manipulate light in ways unattainable by natural materials. Recent advances have leveraged computational optimization, machine learning, and deep learning to automate their design. However, existing approaches exhibit two fundamental limitations: (1) they often restrict the model to generating only a subset of design parameters, and (2) they rely on heavily downsampled spectral targets, which compromises both the novelty and accuracy of the resulting structures. The core challenge lies in developing a generative model capable of exploring a large, unconstrained design space while precisely capturing the intricate physical relationships between material parameters and their high-resolution spectral responses. In this paper, we introduce MetaDiT, a novel framework for high-fidelity metasurface design that addresses these limitations. Our approach leverages a robust spectrum encoder pretrained with contrastive learning, providing strong conditional guidance to a Diffusion Transformer-based backbone. Experiments demonstrate that MetaDiT outperforms existing baselines in spectral accuracy, we further validate our method through extensive ablation studies. Our code and model weights will be open-sourced to facilitate future research.

Strategies for the generation of periodic discrete structures with identical two-point correlation are developed. Starting from a pair of root structures, which are not related by translation, phase inversion or axis reflections, child structures of arbitrary resolution (i.e., pixel or voxel numbers) and number of phases (i.e., material phases/species) can be generated by means of trivial embedding based phase extension, application of kernels and/or phase coalescence, such that the generated structures inherit the two-point-correlation equivalence. Proofs of the inheritance property are provided by means of the Discrete Fourier Transform theory. A Python 3 implementation of the results is offered by the authors through the Github repository https://github.com/DataAnalyticsEngineering/EQ2PC in order to make the provided results reproducible and useful for all interested readers. Examples for the generation of structures are demonstrated, together with applications in the homogenization theory of periodic media.

Crystal structure generation is a foundational challenge in materials discovery, particularly in designing functional inorganic crystalline materials with desired properties. Most existing diffusion-based generative models for crystals rely on complex, hand-crafted priors and modular architectures to separately model atom types, atomic positions, and lattice parameters. These methods often require customized diffusion processes and conditional denoising, which can introduce additional model complexities and inconsistencies. Here we introduce DiffCrysGen, a fully data-driven, score-based diffusion model that jointly learns the distribution of all structural components in crystalline materials. With crystal structure representation as unified 2D matrices, DiffCrysGen bypasses the need for task-specific priors or decoupled modules, enabling end-to-end generation of atom types, fractional coordinates, and lattice parameters within a single framework. Our model learns crystallographic symmetry and chemical validity directly from large-scale datasets, allowing it to scale to complex materials discovery tasks. As a demonstration, we applied DiffCrysGen to the design of rare-earth-free magnetic materials with high saturation magnetization, showing its effectiveness in generating stable, diverse, and property-aligned candidates for sustainable magnet applications.

Generating the periodic structure of stable materials is a long-standing challenge for the material design community. This task is difficult because stable materials only exist in a low-dimensional subspace of all possible periodic arrangements of atoms: 1) the coordinates must lie in the local energy minimum defined by quantum mechanics, and 2) global stability also requires the structure to follow the complex, yet specific bonding preferences between different atom types. Existing methods fail to incorporate these factors and often lack proper invariances. We propose a Crystal Diffusion Variational Autoencoder (CDVAE) that captures the physical inductive bias of material stability. By learning from the data distribution of stable materials, the decoder generates materials in a diffusion process that moves atomic coordinates towards a lower energy state and updates atom types to satisfy bonding preferences between neighbors. Our model also explicitly encodes interactions across periodic boundaries and respects permutation, translation, rotation, and periodic invariances. We significantly outperform past methods in three tasks: 1) reconstructing the input structure, 2) generating valid, diverse, and realistic materials, and 3) generating materials that optimize a specific property. We also provide several standard datasets and evaluation metrics for the broader machine learning community.

This study presents a computational optimisation framework of a hip implant through the development of a functionally graded biomimetic lattice structure, whose design was structurally optimised to limit stress shielding. The optimisation technique was inspired by the inverse of a bone remodelling algorithm, promoting an even stress distribution throughout the design region, by reducing the density and consequently the stiffness, in regions where strain energy was higher than the reference level. The result of the optimisation technique provided a non-uniform graded density distribution field that showed lower density level on the sides of the implant stem, and higher material density around the medial axis of the stem. The optimised material distribution was captured using mapping of a triply periodic minimal surface lattice structure on the implant, which resulted in porous lattice surfaces inside the solid implant. The performance of the porous implant design was evaluated through implementation of a finite element bone remodelling algorithm and comparing the bone response with a femur with fully solid implant model, in terms of stress distribution and mass change. The results of the analysis showed improved bone formation on the bone-implant interface, and enhanced stress transmission to the surrounding bone from the implant.

Quantitative microstructural characterization is fundamental to materials science, where electron micrograph (EM) provides indispensable high-resolution insights. However, progress in deep learning-based EM characterization has been hampered by the scarcity of large-scale, diverse, and expert-annotated datasets, due to acquisition costs, privacy concerns, and annotation complexity. To address this issue, we introduce UniEM-3M, the first large-scale and multimodal EM dataset for instance-level understanding. It comprises 5,091 high-resolution EMs, about 3 million instance segmentation labels, and image-level attribute-disentangled textual descriptions, a subset of which will be made publicly available. Furthermore, we are also releasing a text-to-image diffusion model trained on the entire collection to serve as both a powerful data augmentation tool and a proxy for the complete data distribution. To establish a rigorous benchmark, we evaluate various representative instance segmentation methods on the complete UniEM-3M and present UniEM-Net as a strong baseline model. Quantitative experiments demonstrate that this flow-based model outperforms other advanced methods on this challenging benchmark. Our multifaceted release of a partial dataset, a generative model, and a comprehensive benchmark -- available at huggingface -- will significantly accelerate progress in automated materials analysis.

Diatoms have been described as nanometer-born lithographers because of their ability to create sophisticated three-dimensional amorphous silica exoskeletons. The hierarchical architecture of these structures provides diatoms with mechanical protection and the ability to filter, float, and manipulate light. Therefore, they emerge as an extraordinary model of multifunctional materials from which to draw inspiration. In this paper, we use numerical simulations, analytical models, and experimental tests to unveil the structural and fluid dynamic efficiency of the Coscinodiscus species diatom. Then we propose a novel 3D printable multifunctional biomimetic material for applications such as porous filters, heat exchangers, drug delivery systems, lightweight structures, and robotics. Our results demonstrate the role of Nature as a material designer for efficient and tunable systems and highlight the potential of diatoms for engineering materials innovation. Additionally, the results reported in this paper lay the foundation to extend the structure-property characterization of diatoms.

Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work, we generate a big dataset of structure-property relationships for strut-based lattices. The dataset is made available to the community which can fuel the development of methods anchored in physical principles for the fitting of fourth-order tensors. In addition, we present a higher-order GNN model trained on this dataset. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate its benefits in terms of predictive performance and reduced training requirements. Finally, we demonstrate an example application of the model to an architected material design task. The methods which we developed are applicable to fourth-order tensors beyond elasticity such as piezo-optical tensor etc.

Generative models have recently shown great promise for accelerating the design and discovery of new functional materials. Conditional generation enhances this capacity by allowing inverse design, where specific desired properties can be requested during the generation process. However, conditioning of transformer-based approaches, in particular, is constrained by discrete tokenisation schemes and the risk of catastrophic forgetting during fine-tuning. This work introduces CrystaLLM-π (property injection), a conditional autoregressive framework that integrates continuous property representations directly into the transformer's attention mechanism. Two architectures, Property-Key-Value (PKV) Prefix attention and PKV Residual attention, are presented. These methods bypass inefficient sequence-level tokenisation and preserve foundational knowledge from unsupervised pre-training on Crystallographic Information Files (CIFs) as textual input. We establish the efficacy of these mechanisms through systematic robustness studies and evaluate the framework's versatility across two distinct tasks. First, for structure recovery, the model processes high-dimensional, heterogeneous X-ray diffraction patterns, achieving structural accuracy competitive with specialised models and demonstrating applications to experimental structure recovery and polymorph differentiation. Second, for materials discovery, the model is fine-tuned on a specialised photovoltaic dataset to generate novel, stable candidates validated by Density Functional Theory (DFT). It implicitly learns to target optimal band gap regions for high photovoltaic efficiency, demonstrating a capability to map complex structure-property relationships. CrystaLLM-π provides a unified, flexible, and computationally efficient framework for inverse materials design.

Metamaterials with functional responses can exhibit varying properties under different conditions (e.g., wave-based responses or deformation-induced property variation). This work addresses the rapid inverse design of such metamaterials to meet target qualitative functional behaviors, a challenge due to its intractability and non-unique solutions. Unlike data-intensive and non-interpretable deep-learning-based methods, we propose the Random-forest-based Interpretable Generative Inverse Design (RIGID), a single-shot inverse design method for fast generation of metamaterial designs with on-demand functional behaviors. RIGID leverages the interpretability of a random forest-based "designrightarrowresponse" forward model, eliminating the need for a more complex "responserightarrowdesign" inverse model. Based on the likelihood of target satisfaction derived from the trained random forest, one can sample a desired number of design solutions using Markov chain Monte Carlo methods. We validate RIGID on acoustic and optical metamaterial design problems, each with fewer than 250 training samples. Compared to the genetic algorithm-based design generation approach, RIGID generates satisfactory solutions that cover a broader range of the design space, allowing for better consideration of additional figures of merit beyond target satisfaction. This work offers a new perspective on solving on-demand inverse design problems, showcasing the potential for incorporating interpretable machine learning into generative design under small data constraints.

We consider the matrix composite materials (CM) of either random (statistically homogeneous or inhomogeneous), periodic, or deterministic (neither random nor periodic) structures. CMs exhibit linear or nonlinear behavior, coupled or uncoupled multi-physical phenomena, locally elastic, weakly nonlocal (strain gradient and stress gradient), or strongly nonlocal (strain-type and displacement-type, peridynamics) phase properties. A modified Computational Analytical Micromechanics (CAM) approach introduces an exact Additive General Integral Equation (AGIE) for CMs of any structure and phase properties mentioned above. The unified iteration solution of static AGIEs is adapted to the body force with compact support serving as a fundamentally new universal training parameter. The approach also establishes a critical threshold for filtering out unsuitable sub-datasets of effective parameters through a novel Representative Volume Element (RVE) concept, which extends Hill's classical framework. This RVE concept eliminates sample size, boundary layer, and edge effects, making it applicable to CMs of any structure and phase properties, regardless of local or nonlocal, linear or nonlinear. Incorporating this new RVE concept into machine learning and neural network techniques enables the construction of any unpredefined surrogate nonlocal operators. The methodology is structured as a modular, block-based framework, allowing independent development and refinement of software components. This flexible, robust AGIE-CAM framework integrates data-driven, multi-scale, and multi-physics modeling, accelerating research in CM of any microtopology and phase properties considered. The AGIE-CAM framework represents a groundbreaking paradigm shift in the micromechanics of composites, redefining the very philosophy that underpins our understanding of their behavior at the microscopic level.

Stable diffusion models represent the state-of-the-art in data synthesis across diverse domains and hold transformative potential for applications in science and engineering, e.g., by facilitating the discovery of novel solutions and simulating systems that are computationally intractable to model explicitly. While there is increasing effort to incorporate physics-based constraints into generative models, existing techniques are either limited in their applicability to latent diffusion frameworks or lack the capability to strictly enforce ___domain-specific constraints. To address this limitation this paper proposes a novel integration of stable diffusion models with constrained optimization frameworks, enabling the generation of outputs satisfying stringent physical and functional requirements. The effectiveness of this approach is demonstrated through material design experiments requiring adherence to precise morphometric properties, challenging inverse design tasks involving the generation of materials inducing specific stress-strain responses, and copyright-constrained content generation tasks. All code has been released at https://github.com/RAISELab-atUVA/Constrained-Stable-Diffusion.

Data-driven materials discovery requires large-scale experimental datasets, yet most of the information remains trapped in unstructured literature. Existing extraction efforts often focus on a limited set of features and have not addressed the integrated composition-processing-microstructure-property relationships essential for understanding materials behavior, thereby posing challenges for building comprehensive databases. To address this gap, we propose a multi-stage information extraction pipeline powered by large language models, which captures 47 features spanning composition, processing, microstructure, and properties exclusively from experimentally reported materials. The pipeline integrates iterative extraction with source tracking to enhance both accuracy and reliability. Evaluations at the feature level (independent attributes) and tuple level (interdependent features) yielded F1 scores around 0.96. Compared with single-pass extraction without source tracking, our approach improved F1 scores of microstructure category by 10.0% (feature level) and 13.7% (tuple level), and reduced missed materials from 49 to 13 out of 396 materials in 100 articles on precipitate-containing multi-principal element alloys (miss rate reduced from 12.4% to 3.3%). The pipeline enables scalable and efficient literature mining, producing databases with high precision, minimal omissions, and zero false positives. These datasets provide trustworthy inputs for machine learning and materials informatics, while the modular design generalizes to diverse material classes, enabling comprehensive materials information extraction.

The recently proposed term "heterostructured (HS) materials" serves as an umbrella classification encompassing a wide range of materials that hold great promise for enhanced mechanical properties. Most HS materials exhibit back-stress strengthening, as is typical for all plastically non-homogeneous materials. To better embody the distinctiveness of materials crafted via innovative heterostructuring, here we introduce the concept of "structural gradient hardening" (SGH), which captures an essential feature of HS materials and complements traditional strengthening mechanisms. SGH refers to the extra strengthening that arises from a characteristic gradient structure introduced by heterostructuring, beyond what is predicted by the rule of mixtures. This distinction is useful, as the overall back stress can in fact be partitioned into Type I and Type II components, with the latter specifically quantifying the extra hardening originating from the structural and strain gradients established by heterostructuring, as articulated in this Viewpoint article.

Materials discovery is a cornerstone of modern technological advancement, yet it remains constrained by traditional trial-and-error paradigms and the inherent bias of human intuition. Artificial intelligence (AI) has emerged as a transformative tool in materials science by effectively modeling structure-property relationships. Despite substantial efforts to enhance model expressiveness, data efficiency remains an equally critical challenge, given the limited availability of experimental and computational resources. Active learning (AL), as a data-driven machine learning paradigm, has shown great promise for discovering novel materials and enabling the efficient navigation of vast materials spaces. In this review, we follow the evolution of sampling strategy design techniques in AL, from Bayesian optimization to advanced deep learning-based strategies. We then highlight how AL enhances data efficiency across various data regimes, ranging from task-specific settings with limited data to the development of general-purpose datasets and large-scale models. We further provide a systematic overview of AL applications throughout the materials research pipeline, including computational simulation, composition and structural design, process optimization, and self-driving laboratory systems. Finally, we pinpoint key challenges and future perspectives of AL in materials discovery.

Inverse design of solid-state materials with desired properties represents a formidable challenge in materials science. Although recent generative models have demonstrated potential, their adoption has been hindered by limitations such as inefficiency, architectural constraints and restricted open-source availability. The representation of crystal structures using the SLICES (Simplified Line-Input Crystal-Encoding System) notation as a string of characters enables the use of state-of-the-art natural language processing models, such as Transformers, for crystal design. Drawing inspiration from the success of GPT models in generating coherent text, we trained a generative Transformer on the next-token prediction task to generate solid-state materials with targeted properties. We demonstrate MatterGPT's capability to generate de novo crystal structures with targeted single properties, including both lattice-insensitive (formation energy) and lattice-sensitive (band gap) properties. Furthermore, we extend MatterGPT to simultaneously target multiple properties, addressing the complex challenge of multi-objective inverse design of crystals. Our approach showcases high validity, uniqueness, and novelty in generated structures, as well as the ability to generate materials with properties beyond the training data distribution. This work represents a significant step forward in computational materials discovery, offering a powerful and open tool for designing materials with tailored properties for various applications in energy, electronics, and beyond.

Accelerating material discovery holds the potential to greatly help mitigate the climate crisis. Discovering new solid-state materials such as electrocatalysts, super-ionic conductors or photovoltaic materials can have a crucial impact, for instance, in improving the efficiency of renewable energy production and storage. In this paper, we introduce Crystal-GFN, a generative model of crystal structures that sequentially samples structural properties of crystalline materials, namely the space group, composition and lattice parameters. This ___domain-inspired approach enables the flexible incorporation of physical and structural hard constraints, as well as the use of any available predictive model of a desired physicochemical property as an objective function. To design stable materials, one must target the candidates with the lowest formation energy. Here, we use as objective the formation energy per atom of a crystal structure predicted by a new proxy machine learning model trained on MatBench. The results demonstrate that Crystal-GFN is able to sample highly diverse crystals with low (median -3.1 eV/atom) predicted formation energy.

Alloy discovery is central to advancing modern industry but remains hindered by the vastness of compositional design space and the costly validation. Here, we present AutoMAT, a hierarchical and autonomous framework grounded in and validated by experiments, which integrates large language models, automated CALPHAD-based simulations, and AI-driven search to accelerate alloy design. Spanning the entire pipeline from ideation to validation, AutoMAT achieves high efficiency, accuracy, and interpretability without the need for manually curated large datasets. In a case study targeting a lightweight, high-strength alloy, AutoMAT identifies a titanium alloy with 8.1% lower density and comparable yield strength relative to the state-of-the-art reference, achieving the highest specific strength among all comparisons. In a second case targeting high-yield-strength high-entropy alloys, AutoMAT achieves a 28.2% improvement in yield strength over the base alloy. In both cases, AutoMAT reduces the discovery timeline from years to weeks, illustrating its potential as a scalable and versatile platform for next-generation alloy design.

Structural topology optimization (TO) is central to engineering design but remains computationally intensive due to complex physics and hard constraints. Existing deep-learning methods are limited to fixed square grids, a few hand-coded boundary conditions, and post-hoc optimization, preventing general deployment. We introduce Optimize Any Topology (OAT), a foundation-model framework that directly predicts minimum-compliance layouts for arbitrary aspect ratios, resolutions, volume fractions, loads, and fixtures. OAT combines a resolution- and shape-agnostic autoencoder with an implicit neural-field decoder and a conditional latent-diffusion model trained on OpenTO, a new corpus of 2.2 million optimized structures covering 2 million unique boundary-condition configurations. On four public benchmarks and two challenging unseen tests, OAT lowers mean compliance up to 90% relative to the best prior models and delivers sub-1 second inference on a single GPU across resolutions from 64 x 64 to 256 x 256 and aspect ratios as high as 10:1. These results establish OAT as a general, fast, and resolution-free framework for physics-aware topology optimization and provide a large-scale dataset to spur further research in generative modeling for inverse design. Code & data can be found at https://github.com/ahnobari/OptimizeAnyTopology.

We report a flexible multi-modal mechanics language model, MeLM, applied to solve various nonlinear forward and inverse problems, that can deal with a set of instructions, numbers and microstructure data. The framework is applied to various examples including bio-inspired hierarchical honeycomb design, carbon nanotube mechanics, and protein unfolding. In spite of the flexible nature of the model-which allows us to easily incorporate diverse materials, scales, and mechanical features-it performs well across disparate forward and inverse tasks. Based on an autoregressive attention-model, MeLM effectively represents a large multi-particle system consisting of hundreds of millions of neurons, where the interaction potentials are discovered through graph-forming self-attention mechanisms that are then used to identify relationships from emergent structures, while taking advantage of synergies discovered in the training data. We show that the model can solve complex degenerate mechanics design problems and determine novel material architectures across a range of hierarchical levels, providing an avenue for materials discovery and analysis. Looking beyond the demonstrations reported in this paper, we discuss other opportunities in applied mechanics and general considerations about the use of large language models in modeling, design, and analysis that can span a broad spectrum of material properties from mechanical, thermal, optical, to electronic.

The performance of advanced materials for extreme environments is underpinned by their microstructure, including the size and distribution of reinforcing phases. Chromium-based superalloys are a recently proposed alternative to conventional face-centred-cubic superalloys for high-temperature applications, such as Concentrated Solar Power, and their development requires efficient measurement of precipitate volume fraction and size distribution from electron microscopy images. Traditional fixed-threshold image processing is sensitive to background noise, generalises poorly across materials, and requires substantial manual measurement effort. To address these bottlenecks, this study proposes DT-SegNet, an end-to-end two-stage deep learning scheme based on YOLOv5 and SegFormer for object detection and segmentation in electron microscopy images. The approach combines the training efficiency of convolutional neural networks at the detection stage with the segmentation accuracy of a Vision Transformer. Numerical experiments show that DT-SegNet substantially outperforms state-of-the-art segmentation tools offered by Weka and ilastik across metrics including accuracy, precision, recall, and F1-score. The model provides a useful tool for alloy-development microstructure examinations and helps address the large datasets associated with high-throughput alloy development.

Materials discovery and design aim to find compositions and structures with desirable properties over highly complex and diverse physical spaces. Traditional solutions, such as high-throughput simulations or machine learning, often rely on complex descriptors, which hinder generalizability and transferability across different material systems. Moreover, These descriptors may inadequately represent macro-scale material properties, which are influenced by structural imperfections and compositional variations in real-world samples, thus limiting their practical applicability. To address these challenges, we propose DARWIN 1.5, the largest open-source large language model tailored for materials science. By leveraging natural language as input, DARWIN eliminates the need for task-specific descriptors and enables a flexible, unified approach to material property prediction and discovery. Our approach integrates 6M material ___domain papers and 21 experimental datasets from 49,256 materials across modalities while enabling cross-task knowledge transfer. The enhanced model achieves up to 59.1% improvement in prediction accuracy over the base LLaMA-7B architecture and outperforms SOTA machine learning approaches across 8 materials design tasks. These results establish LLMs as a promising foundation for developing versatile and scalable models in materials science.

Metamaterials, engineered materials with architected structures across multiple length scales, offer unprecedented and tunable mechanical properties that surpass those of conventional materials. However, leveraging advanced machine learning (ML) for metamaterial discovery is hindered by three fundamental challenges: (C1) Data Heterogeneity Challenge arises from heterogeneous data sources, heterogeneous composition scales, and heterogeneous structure categories; (C2) Model Complexity Challenge stems from the intricate geometric constraints of ML models, which complicate their adaptation to metamaterial structures; and (C3) Human-AI Collaboration Challenge comes from the "dual black-box'' nature of sophisticated ML models and the need for intuitive user interfaces. To tackle these challenges, we introduce a unified framework, named MetamatBench, that operates on three levels. (1) At the data level, we integrate and standardize 5 heterogeneous, multi-modal metamaterial datasets. (2) The ML level provides a comprehensive toolkit that adapts 17 state-of-the-art ML methods for metamaterial discovery. It also includes a comprehensive evaluation suite with 12 novel performance metrics with finite element-based assessments to ensure accurate and reliable model validation. (3) The user level features a visual-interactive interface that bridges the gap between complex ML techniques and non-ML researchers, advancing property prediction and inverse design of metamaterials for research and applications. MetamatBench offers a unified platform deployed at http://zhoulab-1.cs.vt.edu:5550 that enables machine learning researchers and practitioners to develop and evaluate new methodologies in metamaterial discovery. For accessibility and reproducibility, we open-source our benchmark and the codebase at https://github.com/cjpcool/Metamaterial-Benchmark.

Engineering design optimization seeks to automatically determine the shapes, topologies, or parameters of components that maximize performance under given conditions. This process often depends on physics-based simulations, which are difficult to install, computationally expensive, and require ___domain-specific expertise. To mitigate these challenges, we introduce EngiBench, the first open-source library and datasets spanning diverse domains for data-driven engineering design. EngiBench provides a unified API and a curated set of benchmarks -- covering aeronautics, heat conduction, photonics, and more -- that enable fair, reproducible comparisons of optimization and machine learning algorithms, such as generative or surrogate models. We also release EngiOpt, a companion library offering a collection of such algorithms compatible with the EngiBench interface. Both libraries are modular, letting users plug in novel algorithms or problems, automate end-to-end experiment workflows, and leverage built-in utilities for visualization, dataset generation, feasibility checks, and performance analysis. We demonstrate their versatility through experiments comparing state-of-the-art techniques across multiple engineering design problems, an undertaking that was previously prohibitively time-consuming to perform. Finally, we show that these problems pose significant challenges for standard machine learning methods due to highly sensitive and constrained design manifolds.

We introduce Multi-Objective Counterfactuals for Design (MCD), a novel method for counterfactual optimization in design problems. Counterfactuals are hypothetical situations that can lead to a different decision or choice. In this paper, the authors frame the counterfactual search problem as a design recommendation tool that can help identify modifications to a design, leading to better functional performance. MCD improves upon existing counterfactual search methods by supporting multi-objective queries, which are crucial in design problems, and by decoupling the counterfactual search and sampling processes, thus enhancing efficiency and facilitating objective tradeoff visualization. The paper demonstrates MCD's core functionality using a two-dimensional test case, followed by three case studies of bicycle design that showcase MCD's effectiveness in real-world design problems. In the first case study, MCD excels at recommending modifications to query designs that can significantly enhance functional performance, such as weight savings and improvements to the structural safety factor. The second case study demonstrates that MCD can work with a pre-trained language model to suggest design changes based on a subjective text prompt effectively. Lastly, the authors task MCD with increasing a query design's similarity to a target image and text prompt while simultaneously reducing weight and improving structural performance, demonstrating MCD's performance on a complex multimodal query. Overall, MCD has the potential to provide valuable recommendations for practitioners and design automation researchers looking for answers to their ``What if'' questions by exploring hypothetical design modifications and their impact on multiple design objectives. The code, test problems, and datasets used in the paper are available to the public at decode.mit.edu/projects/counterfactuals/.

This paper presents a data-driven, task-specific paradigm for experimental design, to shorten acquisition time, reduce costs, and accelerate the deployment of imaging devices. Current approaches in experimental design focus on model-parameter estimation and require specification of a particular model, whereas in imaging, other tasks may drive the design. Furthermore, such approaches often lead to intractable optimization problems in real-world imaging applications. Here we present a new paradigm for experimental design that simultaneously optimizes the design (set of image channels) and trains a machine-learning model to execute a user-specified image-analysis task. The approach obtains data densely-sampled over the measurement space (many image channels) for a small number of acquisitions, then identifies a subset of channels of prespecified size that best supports the task. We propose a method: TADRED for TAsk-DRiven Experimental Design in imaging, to identify the most informative channel-subset whilst simultaneously training a network to execute the task given the subset. Experiments demonstrate the potential of TADRED in diverse imaging applications: several clinically-relevant tasks in magnetic resonance imaging; and remote sensing and physiological applications of hyperspectral imaging. Results show substantial improvement over classical experimental design, two recent application-specific methods within the new paradigm, and state-of-the-art approaches in supervised feature selection. We anticipate further applications of our approach. Code is available: https://github.com/sbb-gh/experimental-design-multichannel

Multi-cellular robot design aims to create robots comprised of numerous cells that can be efficiently controlled to perform diverse tasks. Previous research has demonstrated the ability to generate robots for various tasks, but these approaches often optimize robots directly in the vast design space, resulting in robots with complicated morphologies that are hard to control. In response, this paper presents a novel coarse-to-fine method for designing multi-cellular robots. Initially, this strategy seeks optimal coarse-grained robots and progressively refines them. To mitigate the challenge of determining the precise refinement juncture during the coarse-to-fine transition, we introduce the Hyperbolic Embeddings for Robot Design (HERD) framework. HERD unifies robots of various granularity within a shared hyperbolic space and leverages a refined Cross-Entropy Method for optimization. This framework enables our method to autonomously identify areas of exploration in hyperbolic space and concentrate on regions demonstrating promise. Finally, the extensive empirical studies on various challenging tasks sourced from EvoGym show our approach's superior efficiency and generalization capability.

Crystalline materials are a fundamental component in next-generation technologies, yet modeling their distribution presents unique computational challenges. Of the plausible arrangements of atoms in a periodic lattice only a vanishingly small percentage are thermodynamically stable, which is a key indicator of the materials that can be experimentally realized. Two fundamental tasks in this area are to (a) predict the stable crystal structure of a known composition of elements and (b) propose novel compositions along with their stable structures. We present FlowMM, a pair of generative models that achieve state-of-the-art performance on both tasks while being more efficient and more flexible than competing methods. We generalize Riemannian Flow Matching to suit the symmetries inherent to crystals: translation, rotation, permutation, and periodic boundary conditions. Our framework enables the freedom to choose the flow base distributions, drastically simplifying the problem of learning crystal structures compared with diffusion models. In addition to standard benchmarks, we validate FlowMM's generated structures with quantum chemistry calculations, demonstrating that it is about 3x more efficient, in terms of integration steps, at finding stable materials compared to previous open methods.

Structural vibrations are a source of unwanted noise in engineering systems like cars, trains or airplanes. Minimizing these vibrations is crucial for improving passenger comfort. This work presents a novel design optimization approach based on guided flow matching for reducing vibrations by placing beadings (indentations) in plate-like structures. Our method integrates a generative flow matching model and a surrogate model trained to predict structural vibrations. During the generation process, the flow matching model pushes towards manufacturability while the surrogate model pushes to low-vibration solutions. The flow matching model and its training data implicitly define the design space, enabling a broader exploration of potential solutions as no optimization of manually-defined design parameters is required. We apply our method to a range of differentiable optimization objectives, including direct optimization of specific eigenfrequencies through careful construction of the objective function. Results demonstrate that our method generates diverse and manufacturable plate designs with reduced structural vibrations compared to designs from random search, a criterion-based design heuristic and genetic optimization. The code and data are available from https://github.com/ecker-lab/Optimizing_Vibrating_Plates.

CONSPECTUS: Two-dimensional (2D) compound materials are promising materials for use in electronics, optoelectronics, flexible devices, etc. because they are ultrathin and cover a wide range of properties. Among all methods to prepare 2D materials, chemical vapor deposition (CVD) is promising because it produces materials with a high quality and reasonable cost. So far, much efforts have been made to produce 2D compound materials with large ___domain size, controllable number of layers, fast-growth rate, and high quality features, etc. However, due to the complicated growth mechanism like sublimation and diffusion processes of multiple precursors, maintaining the controllability, repeatability, and high quality of CVD grown 2D binary and ternary materials is still a big challenge, which prevents their widespread use. Here, taking 2D transition metal dichalcogenides (TMDCs) as examples, we review current progress and highlight some promising growth strategies for the growth of 2D compound materials. The key technology issues which affect the CVD process, including non-metal precursor, metal precursor, substrate engineering, temperature, and gas flow, are discussed. Also, methods in improving the quality of CVD-grown 2D materials and current understanding on their growth mechanism are highlighted. Finally, challenges and opportunities in this field are proposed. We believe this review will guide the future design of controllable CVD systems for the growth of 2D compound materials with good controllability and high quality, laying the foundations for their potential applications.

Designing metal-organic frameworks (MOFs) with novel chemistries is a longstanding challenge due to their large combinatorial space and complex 3D arrangements of the building blocks. While recent deep generative models have enabled scalable MOF generation, they assume (1) a fixed set of building blocks and (2) known local 3D coordinates of building blocks. However, this limits their ability to (1) design novel MOFs and (2) generate the structure using novel building blocks. We propose a two-stage MOF generation framework that overcomes these limitations by modeling both chemical and geometric degrees of freedom. First, we train an SMILES-based autoregressive model to generate metal and organic building blocks, paired with a cheminformatics toolkit for 3D structure initialization. Second, we introduce a flow matching model that predicts translations, rotations, and torsional angles to assemble the blocks into valid 3D frameworks. Our experiments demonstrate improved reconstruction accuracy, the generation of valid, novel, and unique MOFs, and the ability to create novel building blocks. Our code is available at https://github.com/nayoung10/MOFFlow-2.

Large language models (LLMs) such as generative pretrained transformers (GPTs) have shown potential for various commercial applications, but their applicability for materials design remains underexplored. In this article, we introduce AtomGPT, a model specifically developed for materials design based on transformer architectures, to demonstrate the capability for both atomistic property prediction and structure generation. We show that a combination of chemical and structural text descriptions can efficiently predict material properties with accuracy comparable to graph neural network models, including formation energies, electronic bandgaps from two different methods and superconducting transition temperatures. Furthermore, we demonstrate that AtomGPT can generate atomic structures for tasks such as designing new superconductors, with the predictions validated through density functional theory calculations. This work paves the way for leveraging LLMs in forward and inverse materials design, offering an efficient approach to the discovery and optimization of materials.

Machine-learning generative methods for material design are constructed by representing a given chemical structure, either a solid or a molecule, over appropriate atomic features, generally called structural descriptors. These must be fully descriptive of the system, must facilitate the training process and must be invertible, so that one can extract the atomic configurations corresponding to the output of the model. In general, this last requirement is not automatically satisfied by the most efficient structural descriptors, namely the representation is not directly invertible. Such drawback severely limits our freedom of choice in selecting the most appropriate descriptors for the problem, and thus our flexibility to construct generative models. In this work, we present a general optimization method capable of inverting any local many-body descriptor of the chemical environment, back to a cartesian representation. The algorithm is then implemented together with the bispectrum representation of the local structure and demonstrated for a number of molecules. The scheme presented here, thus, represents a general approach to the inversion of structural descriptors, enabling the construction of efficient structural generative models.

Recent advances in photonic optimization have enabled calculation of performance bounds for a wide range of electromagnetic objectives, albeit restricted to single-material systems. Motivated by growing theoretical interest and fabrication advances, we present a framework to bound the performance of photonic heterostructures and apply it to investigate maximum absorption characteristics of multilayer films and compact, free-form multi-material scatterers. Limits predict trends seen in topology-optimized geometries -- often coming within factors of two of specific designs -- and may be exploited in conjunction with inverse designs to predict when heterostructures are expected to outperform their optimal single-material counterparts.

High throughput experimentation tools, machine learning (ML) methods, and open material databases are radically changing the way new materials are discovered. From the experimentally driven approach in the past, we are moving quickly towards the artificial intelligence (AI) driven approach, realizing the 'inverse design' capabilities that allow the discovery of new materials given the desired properties. This review aims to discuss different principles of AI-driven generative models that are applicable for materials discovery, including different materials representations available for this purpose. We will also highlight specific applications of generative models in designing new catalysts, semiconductors, polymers, or crystals while addressing challenges such as data scarcity, computational cost, interpretability, synthesizability, and dataset biases. Emerging approaches to overcome limitations and integrate AI with experimental workflows will be discussed, including multimodal models, physics informed architectures, and closed-loop discovery systems. This review aims to provide insights for researchers aiming to harness AI's transformative potential in accelerating materials discovery for sustainability, healthcare, and energy innovation.

High-throughput data generation methods and machine learning (ML) algorithms have given rise to a new era of computational materials science by learning relationships among composition, structure, and properties and by exploiting such relations for design. However, to build these connections, materials data must be translated into a numerical form, called a representation, that can be processed by a machine learning model. Datasets in materials science vary in format (ranging from images to spectra), size, and fidelity. Predictive models vary in scope and property of interests. Here, we review context-dependent strategies for constructing representations that enable the use of materials as inputs or outputs of machine learning models. Furthermore, we discuss how modern ML techniques can learn representations from data and transfer chemical and physical information between tasks. Finally, we outline high-impact questions that have not been fully resolved and thus, require further investigation.

Large Language Models (LLMs) promise to accelerate discovery by reasoning across the expanding scientific landscape. Yet, the challenge is no longer access to information but connecting it in meaningful, ___domain-spanning ways. In materials science, where innovation demands integrating concepts from molecular chemistry to mechanical performance, this is especially acute. Neither humans nor single-agent LLMs can fully contend with this torrent of information, with the latter often prone to hallucinations. To address this bottleneck, we introduce a multi-agent framework guided by large-scale knowledge graphs to find sustainable substitutes for per- and polyfluoroalkyl substances (PFAS)-chemicals currently under intense regulatory scrutiny. Agents in the framework specialize in problem decomposition, evidence retrieval, design parameter extraction, and graph traversal, uncovering latent connections across distinct knowledge pockets to support hypothesis generation. Ablation studies show that the full multi-agent pipeline outperforms single-shot prompting, underscoring the value of distributed specialization and relational reasoning. We demonstrate that by tailoring graph traversal strategies, the system alternates between exploitative searches focusing on ___domain-critical outcomes and exploratory searches surfacing emergent cross-connections. Illustrated through the exemplar of biomedical tubing, the framework generates sustainable PFAS-free alternatives that balance tribological performance, thermal stability, chemical resistance, and biocompatibility. This work establishes a framework combining knowledge graphs with multi-agent reasoning to expand the materials design space, showcasing several initial design candidates to demonstrate the approach.

Parametric computer-aided design (CAD) tools are the predominant way that engineers specify physical structures, from bicycle pedals to airplanes to printed circuit boards. The key characteristic of parametric CAD is that design intent is encoded not only via geometric primitives, but also by parameterized constraints between the elements. This relational specification can be viewed as the construction of a constraint program, allowing edits to coherently propagate to other parts of the design. Machine learning offers the intriguing possibility of accelerating the design process via generative modeling of these structures, enabling new tools such as autocompletion, constraint inference, and conditional synthesis. In this work, we present such an approach to generative modeling of parametric CAD sketches, which constitute the basic computational building blocks of modern mechanical design. Our model, trained on real-world designs from the SketchGraphs dataset, autoregressively synthesizes sketches as sequences of primitives, with initial coordinates, and constraints that reference back to the sampled primitives. As samples from the model match the constraint graph representation used in standard CAD software, they may be directly imported, solved, and edited according to downstream design tasks. In addition, we condition the model on various contexts, including partial sketches (primers) and images of hand-drawn sketches. Evaluation of the proposed approach demonstrates its ability to synthesize realistic CAD sketches and its potential to aid the mechanical design workflow.

Recent advances in synthetic methods enable designing subunits that self-assemble into structures with well-defined sizes and architectures, but yields are frequently suppressed by the formation of off-target metastable structures. Increasing the complexity (number of distinct inter-subunit interaction types) can inhibit off-target structures, but leads to slower kinetics and higher synthesis costs. Here, we use icosahedral shells formed of programmable triangular subunits as a model system, and identify design principles that produce the highest target yield at the lowest complexity. We use a symmetry-based construction to create a range of design complexities, starting from the maximal symmetry Caspar-Klug assembly up to the fully addressable, zero-symmetry assembly. Kinetic Monte Carlo simulations reveal that the most prominent defects leading to off-target assemblies are a class of disclinations. We derive symmetry-based rules for identifying the optimal (lowest-complexity, highest-symmetry) design that inhibits these disclinations, leading to robust, high-fidelity assembly of targets with arbitrarily large sizes. Optimal complexity varies non-monotonically with target size, with `magic' sizes appearing for high-symmetry designs in which symmetry axes do not intersect vertices of the triangular net. The optimal designs at magic sizes require 12 times fewer inequivalent interaction-types than the (minimal symmetry) fully addressable construction.

Data-driven engineering design is constrained by the lack of large-scale 3D datasets that pair geometry with physics-based performance labels. In particular, existing 3D data augmentation techniques have limitations in preserving subtle and diverse geometric variations, and it remains difficult to automate the subsequent simulation-labeling process, where boundary conditions vary depending on the generated geometry. We present DeepJEB++, a foundation-model-driven data-augmentation framework that expands a small seed set of jet engine brackets into a large, simulation-labeled 3D dataset under constrained resources. Our key idea is to augment in the data-rich 2D latent space, then transfer to 3D. In Stage 1, we fine-tune a pretrained 2D latent diffusion model on multi-view renders and synthesize novel views by latent interpolation, retaining manufacturable designs through a vision-language-model (VLM) quality filter. In Stage 2, the validated images are lifted to 3D meshes by a ___domain-adapted generative foundation model. In Stage 3, an automated pipeline recognizes the load and bolt interfaces on each mesh and assigns finite-element labels -- mass, stress, and displacement -- without manual intervention. We assess augmentation quality along three intrinsic axes: manufacturability, label fidelity against the SimJEB ground truth, and distributional consistency. Starting from fewer than 400 seed designs, DeepJEB++ yields 15,360 simulation-labeled 3D brackets -- a 40x expansion -- using a single GPU per stage. The dataset will be made publicly available to support reproducible engineering-AI research.

Data-driven design is emerging as a powerful strategy to accelerate engineering innovation. However, its application to vehicle wheel design remains limited due to the lack of large-scale, high-quality datasets that include 3D geometry and physical performance metrics. To address this gap, this study proposes a synthetic design-performance dataset generation framework using generative AI. The proposed framework first generates 2D rendered images using Stable Diffusion, and then reconstructs the 3D geometry through 2.5D depth estimation. Structural simulations are subsequently performed to extract engineering performance data. To further expand the design and performance space, topology optimization is applied, enabling the generation of a more diverse set of wheel designs. The final dataset, named DeepWheel, consists of over 6,000 photo-realistic images and 900 structurally analyzed 3D models. This multi-modal dataset serves as a valuable resource for surrogate model training, data-driven inverse design, and design space exploration. The proposed methodology is also applicable to other complex design domains. The dataset is released under the Creative Commons Attribution-NonCommercial 4.0 International(CC BY-NC 4.0) and is available on the https://www.smartdesignlab.org/datasets

Materials discovery and design are essential for advancing technology across various industries by enabling the development of application-specific materials. Recent research has leveraged Large Language Models (LLMs) to accelerate this process. We explore the potential of LLMs to generate viable hypotheses that, once validated, can expedite materials discovery. Collaborating with materials science experts, we curated a novel dataset from recent journal publications, featuring real-world goals, constraints, and methods for designing real-world applications. Using this dataset, we test LLM-based agents that generate hypotheses for achieving given goals under specific constraints. To assess the relevance and quality of these hypotheses, we propose a novel scalable evaluation metric that emulates the process a materials scientist would use to evaluate a hypothesis critically. Our curated dataset, proposed method, and evaluation framework aim to advance future research in accelerating materials discovery and design with LLMs.

The Materials Genome Initiative catalyzed the proliferation of centralized platforms--SaaS, PaaS, and IaaS--that aggregate computational and experimental resources for accelerated materials discovery. In parallel, breakthroughs in large language models (LLMs) and autonomous agents have created powerful new reasoning capabilities for scientific research. Yet a critical "last mile" problem remains: while we possess world-class models and vast repositories of materials data, we lack the organizational infrastructure to compose these capabilities securely across institutional boundaries. The development of structural and functional materials for harsh service environments--high-temperature alloys, radiation resistant steels, corrosion-resistant coatings--remains characterized by long-term iteration, mechanistic complexity, and high ___domain expertise--demands that exceed both monolithic agent systems and traditional centralized platforms. To address this gap we propose OpenAaaS, an open-source hierarchical and distributed Agent-as-a-Service framework that enables organized multi-agent collaboration for intelligent materials design. OpenAaaS is built on a single foundational principle: code flows, data stays still. A Master Agent plans and decomposes complex research tasks without requiring direct access to subordinate agents' managed data and computational resources. Sub-agents, deployed as near-data execution nodes, retain full sovereignty over local datasets, proprietary algorithms, and specialized hardware. This architecture guarantees that raw data never leaves its ___domain of origin while enabling cross-scale, cross-___domain secure integration of previously isolated materials intelligence silos. We validate the framework through two representative case studies: (i) AlphaAgent, an evidence-grounded materials literature analysis executor that achieves 4.66/5.0 on deep analytical questions against single-pass RAG baselines; and (ii) an ultra-large-scale hexa-high-entropy alloy descriptor database service that demonstrates secure near-data execution and ___domain-specific scientific workflows under strict data-sovereignty constraints. OpenAaaS establishes a principled pathway toward "organized research" via agent collectives, offering a scalable foundation for next-generation materials intelligent design platforms. All source code is available at https://github.com/Wolido/OpenAaaS.

Materials discovery requires navigating vast chemical and structural spaces while satisfying multiple, often conflicting, objectives. We present LLM-guided Evolution for MAterials design (LLEMA), a unified framework that couples the scientific knowledge embedded in large language models with chemistry-informed evolutionary rules and memory-based refinement. At each iteration, an LLM proposes crystallographically specified candidates under explicit property constraints; a surrogate-augmented oracle estimates physicochemical properties; and a multi-objective scorer updates success/failure memories to guide subsequent generations. Evaluated on 14 realistic tasks spanning electronics, energy, coatings, optics, and aerospace, LLEMA discovers candidates that are chemically plausible, thermodynamically stable, and property-aligned, achieving higher hit-rates and stronger Pareto fronts than generative and LLM-only baselines. Ablation studies confirm the importance of rule-guided generation, memory-based refinement, and surrogate prediction. By enforcing synthesizability and multi-objective trade-offs, LLEMA delivers a principled pathway to accelerate practical materials discovery. Code: https://github.com/scientific-discovery/LLEMA

The creation of manufacturable and editable 3D shapes through Computer-Aided Design (CAD) remains a highly manual and time-consuming task, hampered by the complex topology of boundary representations of 3D solids and unintuitive design tools. While most work in the 3D shape generation literature focuses on representations like meshes, voxels, or point clouds, practical engineering applications demand the modifiability and manufacturability of CAD models and the ability for multi-modal conditional CAD model generation. This paper introduces GenCAD, a generative model that employs autoregressive transformers with a contrastive learning framework and latent diffusion models to transform image inputs into parametric CAD command sequences, resulting in editable 3D shape representations. Extensive evaluations demonstrate that GenCAD significantly outperforms existing state-of-the-art methods in terms of the unconditional and conditional generations of CAD models. Additionally, the contrastive learning framework of GenCAD facilitates the retrieval of CAD models using image queries from large CAD databases, which is a critical challenge within the CAD community. Our results provide a significant step forward in highlighting the potential of generative models to expedite the entire design-to-production pipeline and seamlessly integrate different design modalities.

Topology optimization by optimally distributing materials in a given ___domain requires non-gradient optimizers to solve highly complicated problems. However, with hundreds of design variables or more involved, solving such problems would require millions of Finite Element Method (FEM) calculations whose computational cost is huge and impractical. Here we report Self-directed Online Learning Optimization (SOLO) which integrates Deep Neural Network (DNN) with FEM calculations. A DNN learns and substitutes the objective as a function of design variables. A small number of training data is generated dynamically based on the DNN's prediction of the optimum. The DNN adapts to the new training data and gives better prediction in the region of interest until convergence. The optimum predicted by the DNN is proved to converge to the true global optimum through iterations. Our algorithm was tested by four types of problems including compliance minimization, fluid-structure optimization, heat transfer enhancement and truss optimization. It reduced the computational time by 2 ~ 5 orders of magnitude compared with directly using heuristic methods, and outperformed all state-of-the-art algorithms tested in our experiments. This approach enables solving large multi-dimensional optimization problems.

Deep learning methods for material property prediction have been widely explored to advance materials discovery. However, the prevailing pre-train then fine-tune paradigm often fails to address the inherent diversity and disparity of material tasks. To overcome these challenges, we introduce MoMa, a Modular framework for Materials that first trains specialized modules across a wide range of tasks and then adaptively composes synergistic modules tailored to each downstream scenario. Evaluation across 17 datasets demonstrates the superiority of MoMa, with a substantial 14% average improvement over the strongest baseline. Few-shot and continual learning experiments further highlight MoMa's potential for real-world applications. Pioneering a new paradigm of modular material learning, MoMa will be open-sourced to foster broader community collaboration.

The study of biological materials and bio-inspired materials science is well established; however, surprisingly little knowledge has been systematically translated to engineering solutions. To accelerate discovery and guide insights, an open-source autoregressive transformer large language model (LLM), BioinspiredLLM, is reported. The model was finetuned with a corpus of over a thousand peer-reviewed articles in the field of structural biological and bio-inspired materials and can be prompted to recall information, assist with research tasks, and function as an engine for creativity. The model has proven that it is able to accurately recall information about biological materials and is further enhanced with enhanced reasoning ability, as well as with retrieval-augmented generation to incorporate new data during generation that can also help to traceback sources, update the knowledge base, and connect knowledge domains. BioinspiredLLM also has been shown to develop sound hypotheses regarding biological materials design and remarkably so for materials that have never been explicitly studied before. Lastly, the model showed impressive promise in collaborating with other generative artificial intelligence models in a workflow that can reshape the traditional materials design process. This collaborative generative artificial intelligence method can stimulate and enhance bio-inspired materials design workflows. Biological materials are at a critical intersection of multiple scientific fields and models like BioinspiredLLM help to connect knowledge domains.

Inverse design, where we seek to design input variables in order to optimize an underlying objective function, is an important problem that arises across fields such as mechanical engineering to aerospace engineering. Inverse design is typically formulated as an optimization problem, with recent works leveraging optimization across learned dynamics models. However, as models are optimized they tend to fall into adversarial modes, preventing effective sampling. We illustrate that by instead optimizing over the learned energy function captured by the diffusion model, we can avoid such adversarial examples and significantly improve design performance. We further illustrate how such a design system is compositional, enabling us to combine multiple different diffusion models representing subcomponents of our desired system to design systems with every specified component. In an N-body interaction task and a challenging 2D multi-airfoil design task, we demonstrate that by composing the learned diffusion model at test time, our method allows us to design initial states and boundary shapes that are more complex than those in the training data. Our method generalizes to more objects for N-body dataset and discovers formation flying to minimize drag in the multi-airfoil design task. Project website and code can be found at https://github.com/AI4Science-WestlakeU/cindm.

Austenitic 347H stainless steel offers superior mechanical properties and corrosion resistance required for extreme operating conditions such as high temperature. The change in microstructure due to composition and process variations is expected to impact material properties. Identifying microstructural features such as grain boundaries thus becomes an important task in the process-microstructure-properties loop. Applying convolutional neural network (CNN) based deep-learning models is a powerful technique to detect features from material micrographs in an automated manner. Manual labeling of the images for the segmentation task poses a major bottleneck for generating training data and labels in a reliable and reproducible way within a reasonable timeframe. In this study, we attempt to overcome such limitations by utilizing multi-modal microscopy to generate labels directly instead of manual labeling. We combine scanning electron microscopy (SEM) images of 347H stainless steel as training data and electron backscatter diffraction (EBSD) micrographs as pixel-wise labels for grain boundary detection as a semantic segmentation task. We demonstrate that despite producing instrumentation drift during data collection between two modes of microscopy, this method performs comparably to similar segmentation tasks that used manual labeling. Additionally, we find that naïve pixel-wise segmentation results in small gaps and missing boundaries in the predicted grain boundary map. By incorporating topological information during model training, the connectivity of the grain boundary network and segmentation performance is improved. Finally, our approach is validated by accurate computation on downstream tasks of predicting the underlying grain morphology distributions which are the ultimate quantities of interest for microstructural characterization.

Machine learning is a prevalent approach to tame the complexity of design space exploration for ___domain-specific architectures. Using ML for design space exploration poses challenges. First, it's not straightforward to identify the suitable algorithm from an increasing pool of ML methods. Second, assessing the trade-offs between performance and sample efficiency across these methods is inconclusive. Finally, lack of a holistic framework for fair, reproducible, and objective comparison across these methods hinders progress of adopting ML-aided architecture design space exploration and impedes creating repeatable artifacts. To mitigate these challenges, we introduce ArchGym, an open-source gym and easy-to-extend framework that connects diverse search algorithms to architecture simulators. To demonstrate utility, we evaluate ArchGym across multiple vanilla and ___domain-specific search algorithms in designing custom memory controller, deep neural network accelerators, and custom SoC for AR/VR workloads, encompassing over 21K experiments. Results suggest that with unlimited samples, ML algorithms are equally favorable to meet user-defined target specification if hyperparameters are tuned; no solution is necessarily better than another (e.g., reinforcement learning vs. Bayesian methods). We coin the term hyperparameter lottery to describe the chance for a search algorithm to find an optimal design provided meticulously selected hyperparameters. The ease of data collection and aggregation in ArchGym facilitates research in ML-aided architecture design space exploration. As a case study, we show this advantage by developing a proxy cost model with an RMSE of 0.61% that offers a 2,000-fold reduction in simulation time. Code and data for ArchGym is available at https://bit.ly/ArchGym.

We introduce neural lithography to address the 'design-to-manufacturing' gap in computational optics. Computational optics with large design degrees of freedom enable advanced functionalities and performance beyond traditional optics. However, the existing design approaches often overlook the numerical modeling of the manufacturing process, which can result in significant performance deviation between the design and the fabricated optics. To bridge this gap, we, for the first time, propose a fully differentiable design framework that integrates a pre-trained photolithography simulator into the model-based optical design loop. Leveraging a blend of physics-informed modeling and data-driven training using experimentally collected datasets, our photolithography simulator serves as a regularizer on fabrication feasibility during design, compensating for structure discrepancies introduced in the lithography process. We demonstrate the effectiveness of our approach through two typical tasks in computational optics, where we design and fabricate a holographic optical element (HOE) and a multi-level diffractive lens (MDL) using a two-photon lithography system, showcasing improved optical performance on the task-specific metrics.

Spider webs are incredible biological structures, comprising thin but strong silk filament and arranged into complex hierarchical architectures with striking mechanical properties (e.g., lightweight but high strength, achieving diverse mechanical responses). While simple 2D orb webs can easily be mimicked, the modeling and synthesis of 3D-based web structures remain challenging, partly due to the rich set of design features. Here we provide a detailed analysis of the heterogenous graph structures of spider webs, and use deep learning as a way to model and then synthesize artificial, bio-inspired 3D web structures. The generative AI models are conditioned based on key geometric parameters (including average edge length, number of nodes, average node degree, and others). To identify graph construction principles, we use inductive representation sampling of large experimentally determined spider web graphs, to yield a dataset that is used to train three conditional generative models: 1) An analog diffusion model inspired by nonequilibrium thermodynamics, with sparse neighbor representation, 2) a discrete diffusion model with full neighbor representation, and 3) an autoregressive transformer architecture with full neighbor representation. All three models are scalable, produce complex, de novo bio-inspired spider web mimics, and successfully construct graphs that meet the design objectives. We further propose algorithm that assembles web samples produced by the generative models into larger-scale structures based on a series of geometric design targets, including helical and parametric shapes, mimicking, and extending natural design principles towards integration with diverging engineering objectives. Several webs are manufactured using 3D printing and tested to assess mechanical properties.

Modern materials science has historically been founded on combining restricted subsets of the periodic table, favoring high-purity, few-element systems. However, the demands of an emerging circular economy, together with the need to understand materials behavior under planetary and industrial extremes, increasingly require mastering Mendeleev materials - chemically and structurally complex systems that span large portions of the periodic table. In these regimes, current universal machine-learning interatomic potentials often fail, largely due to systematic gaps in traditional training datasets that heavily emphasize low-energy, near-equilibrium structures. We address this limitation by introducing a chemistry-agnostic, information-entropy-maximization protocol for data generation. By decoupling structural sampling from thermodynamic bias, our approach provides a robust physical prior for atomic interactions across the entire periodic table, including regimes far from equilibrium and under extreme conditions. Training a Graph Atomic Cluster Expansion (GRACE) model on the resulting statistically maximized entropy (SMAX) dataset yields markedly improved robustness across a range of stringent benchmarks. These include large-strain phase transformations in tin, defect evolution in tungsten-based alloys, and catalytic reaction barrier prediction. More broadly, our approach establishes a scalable and principled methodology for navigating the vast chemical and configurational space relevant to future materials design. It enables a paradigm of discovery by simulation in which unbiased sampling protocols autonomously resolve emergent structures in multi-elemental mixtures-such as systems containing the nine most abundant elements in the Earth's crust-without reliance on a priori chemical assumptions.

We introduce a novel dataset designed to benchmark the physical and spatial reasoning capabilities of Large Language Models (LLM) based on topology optimization, a method for computing optimal material distributions within a design space under prescribed loads and supports. In this dataset, LLMs are provided with conditions such as 2D boundary, applied forces and supports, and must reason about the resulting optimal material distribution. The dataset includes a variety of tasks, ranging from filling in masked regions within partial structures to predicting complete material distributions. Solving these tasks requires understanding the flow of forces and the required material distribution under given constraints, without access to simulation tools or explicit physical models, challenging models to reason about structural stability and spatial organization. Our dataset targets the evaluation of spatial and physical reasoning abilities in 2D settings, offering a complementary perspective to traditional language and logic benchmarks.

Protein design, a grand challenge of the day, involves optimization on a fitness landscape, and leading methods adopt a model-based approach where a model is trained on a training set (protein sequences and fitness) and proposes candidates to explore next. These methods are challenged by sparsity of high-fitness samples in the training set, a problem that has been in the literature. A less recognized but equally important problem stems from the distribution of training samples in the design space: leading methods are not designed for scenarios where the desired optimum is in a region that is not only poorly represented in training data, but also relatively far from the highly represented low-fitness regions. We show that this problem of "separation" in the design space is a significant bottleneck in existing model-based optimization tools and propose a new approach that uses a novel VAE as its search model to overcome the problem. We demonstrate its advantage over prior methods in robustly finding improved samples, regardless of the imbalance and separation between low- and high-fitness training samples. Our comprehensive benchmark on real and semi-synthetic protein datasets as well as solution design for physics-informed neural networks, showcases the generality of our approach in discrete and continuous design spaces. Our implementation is available at https://github.com/sabagh1994/PGVAE.

Material and product life cycles are based on complex value chains of technology-specific elements. Resource strategy aspects of essential and strategic raw materials have a direct impact on applications of new functionalized materials or the development of novel products. Thus, an urgent challenge of modern materials science is to obtain information about the supply risk and environmental aspects of resource utilization, especially at an early stage of basic research. Combining the fields of materials science, industrial engineering and resource strategy enables a multidisciplinary research approach to identify specific risks within the value chain, aggregated as the so-called resource criticality. Here, we demonstrate a step-by-step criticality assessment in the sector of basic materials research for multifunctional hexagonal manganite YMnO3, which can be a candidate for future electronic systems. Raw material restrictions can be quantitatively identified, even at such an early stage of materials research, from eleven long-term indicators including our new developed Sector Competition Index. This approach for resource strategy for modern material science integrates two objective targets: reduced supply risk and enhanced environmental sustainability of new functionalized materials, showing drawbacks but also benefits towards a sustainable materials research and development.

Every generative model for crystalline materials harbors a critical structure size beyond which its outputs quietly become unreliable -- we call this the extrapolation frontier. Despite its direct consequences for nanomaterial design, this frontier has never been systematically measured. We introduce RADII, a radius-resolved benchmark of {sim}75,000 nanoparticle structures (55-11,298 atoms) that treats radius as a continuous scaling knob to trace generation quality from in-distribution to out-of-distribution regimes under leakage-free splits. RADII provides frontier-specific diagnostics: per-radius error profiles pinpoint each architecture's scaling ceiling, surface-interior decomposition tests whether failures originate at boundaries or in bulk, and cross-metric failure sequencing reveals which aspect of structural fidelity breaks first. Benchmarking five state-of-the-art architectures, we find that: (i) all models degrade by {sim}13% in global positional error beyond training radii, yet local bond fidelity diverges wildly across architectures -- from near-zero to over 2times collapse; (ii) no two architectures share the same failure sequence, revealing the frontier as a multi-dimensional surface shaped by model family; and (iii) well-behaved models obey a power-law scaling exponent αapprox 1/3 whose in-distribution fit accurately predicts out-of-distribution error, making their frontiers quantitatively forecastable. These findings establish output scale as a first-class evaluation axis for geometric generative models. The dataset and code are available at https://github.com/KurbanIntelligenceLab/RADII.

Optical multilayer thin film structures have been widely used in numerous photonic applications. However, existing inverse design methods have many drawbacks because they either fail to quickly adapt to different design targets, or are difficult to suit for different types of structures, e.g., designing for different materials at each layer. These methods also cannot accommodate versatile design situations under different angles and polarizations. In addition, how to benefit practical fabrications and manufacturing has not been extensively considered yet. In this work, we introduce OptoGPT (Opto Generative Pretrained Transformer), a decoder-only transformer, to solve all these drawbacks and issues simultaneously.

OptiWing3D is the first publicly available dataset of high-fidelity shape optimized 3D wing geometries. Existing aerodynamics datasets are either limited to 2D simulations, lack optimization, or derive diversity solely from perturbations to a single baseline design, constraining their application as benchmarks to inverse design approaches and in the study of design diversity. The OptiWing3D dataset addresses these gaps, consisting of 1552 simulations resulting in 776 wing designs initialized from distinct extruded airfoil cross-sections. Additionally, a majority of the optimized wings in the dataset are paired to 2D counterparts optimized under identical conditions, creating the first multi-fidelity aerodynamic shape optimization dataset. Moreover, this structure allows for a direct comparison between 2D and 3D aerodynamic simulations. It is observed that 3D optimized designs diverge most prominently from the 2D-optimized designs near the wingtip, where three-dimensional effects are strongest, a finding made possible by the paired nature of the dataset. Finally, we demonstrate a constraint-aware conditional latent diffusion model capable of generating optimized wings from flow conditions, establishing a baseline for future inverse design approaches. The dataset, containing wing geometries and surface pressure distributions is publicly released to advance research in data-driven aerodynamic design.

Advances in generative artificial intelligence are transforming how metal-organic frameworks (MOFs) are designed and discovered. This Perspective introduces the shift from laborious enumeration of MOF candidates to generative approaches that can autonomously propose and synthesize in the laboratory new porous reticular structures on demand. We outline the progress of employing deep learning models, such as variational autoencoders, diffusion models, and large language model-based agents, that are fueled by the growing amount of available data from the MOF community and suggest novel crystalline materials designs. These generative tools can be combined with high-throughput computational screening and even automated experiments to form accelerated, closed-loop discovery pipelines. The result is a new paradigm for reticular chemistry in which AI algorithms more efficiently direct the search for high-performance MOF materials for clean air and energy applications. Finally, we highlight remaining challenges such as synthetic feasibility, dataset diversity, and the need for further integration of ___domain knowledge.

We review our recent work in the area of autonomous materials research, highlighting the coupling of machine learning methods and models and more problem-aware modeling. We review the general Bayesian framework for closed-loop design employed by many autonomous materials platforms. We then provide examples of our work on such platforms. We finally review our approaches to extend current statistical and ML models to better reflect problem-specific structure including the use of physics-based models and incorporation of operational considerations into the decision-making procedure.

We report a mixture of expert strategy to create fine-tuned large language models using a deep layer-wise token-level approach based on low-rank adaptation (LoRA). Starting with a set of pre-trained LoRA adapters, we propose a gating strategy that uses the hidden states to dynamically mix adapted layers, allowing the resulting X-LoRA model to draw upon different capabilities and create never-before-used deep layer-wise combinations of adaptations are established to solve specific tasks. The design is inspired by the biological principles of universality and diversity, where neural network building blocks are reused in different hierarchical manifestations. Hence, the X-LoRA model can be easily implemented for any existing large language model (LLM) without a need for modifications of the underlying structure. We develop a tailored X-LoRA model that offers scientific capabilities including forward/inverse analysis tasks and enhanced reasoning capability, focused on biomaterial analysis, protein mechanics and design. The impact of this work include access to readily expandable, adaptable and changeable models with strong ___domain knowledge and the capability to integrate across areas of knowledge. With the X-LoRA model featuring experts in biology, mathematics, reasoning, bio-inspired materials, mechanics and materials, chemistry, and protein mechanics we conduct a series of physics-focused case studies. We examine knowledge recall, protein mechanics forward/inverse tasks, protein design, and adversarial agentic modeling including ontological knowledge graphs. The model is capable not only of making quantitative predictions of nanomechanical properties of proteins, but also reasons over the results and correctly predicts likely mechanisms that explain distinct molecular behaviors.

Origami metamaterials typically consist of folded sheets with periodic patterns, conferring them with remarkable mechanical properties. In the context of Continuum Mechanics, the majority of existing predictive methods are mechanism analogs which favor rigid folding and panel bending. While effective in predicting primary deformation modes, existing methods fall short in capturing the full spectrum of deformation of non-rigid foldable origami, such as the emergence of curvature along straight creases, local strain at vertices and warpage in panels. To fully capture the entire deformation spectrum and enhance the accuracy of existing methods, this paper introduces a homogenization framework for origami metamaterials where the faces are modeled as plate elements. Both asymptotic and energy-based homogenization methods are formulated and implemented. As a representative crease pattern, we examine the Miura origami sheet homogenized as an equivalent Kirchhoff-Love plate. The results reveal that certain effective elastic properties are nonlinearly related to both the initial fold angle and the crease stiffness. When benchmarked with results from fully resolved simulations, our framework yields errors up to 12.9\%, while existing models, including the bar-and-hinge model and the rigid-panel model, show up to 161\% error. The differences in errors are associated with the complex modes of crease and panel deformation in non-rigid origami, unexplored by the existing models. This work demonstrates a precise and efficient continuum framework for origami metamaterials as an effective strategy for predicting their elastic properties, understanding their mechanics, and designing their functionalities.

The presence of thermal gradients in alloys often leads to non-uniformity in concentration profiles, which can induce the thermomigration of microstructural features such as precipitates. To investigate such microstructural changes, we present a phase-field model that incorporates coupling between concentration and thermal gradients. First, we simulated the evolution of non-uniform concentration profiles in the single-phase regions of Fe-C and Fe-N alloy systems due to imposed thermal gradients. To validate our model with the classical experiments performed by Darken and Oriani, we studied the evolution of spatially varying concentration profiles where thermal gradients encompass single-phase and two-phase regions. We developed a parameterized thermodynamic description of the two-phase region of a binary alloy to systematically study the effect of interactions between chemically-driven and thermal gradient-driven diffusion of solute on the evolution of precipitates. Our simulations show how thermal gradient, precipitate size, and interparticle distance influence the migration and associated morphological changes of precipitates. The composition profiles and migration rates obtained from single-particle simulations show an exact match with our analytical model. We use twoparticle simulations to show conditions under which thermomigration induces the growth of the smaller particle and shrinkage of the larger one in contrast to the isothermal Ostwald ripening behavior. Our multiparticle simulations show similar behavior during coarsening. Moreover, in the presence of a thermal gradient, there is a shift in the center of mass of the precipitates towards the high-temperature region. Thus, our study offers new insights into the phenomena of microstructure evolution in the presence of thermal gradient.

The relationship between material properties and independent variables such as temperature, external field or time, is usually represented by a curve or surface in a multi-dimensional space. Determining such a curve or surface requires a series of experiments or calculations which are often time and cost consuming. A general strategy uses an appropriate utility function to sample the space to recommend the next optimal experiment or calculation within an active learning loop. However, knowing what the optimal sampling strategy to use to minimize the number of experiments is an outstanding problem. We compare a number of strategies based on directed exploration on several materials problems of varying complexity using a Kriging based model. These include one dimensional curves such as the fatigue life curve for 304L stainless steel and the Liquidus line of the Fe-C phase diagram, surfaces such as the Hartmann 3 function in 3D space and the fitted intermolecular potential for Ar-SH, and a four dimensional data set of experimental measurements for BaTiO3 based ceramics. We also consider the effects of experimental noise on the Hartmann 3 function. We find that directed exploration guided by maximum variance provides better performance overall, converging faster across several data sets. However, for certain problems, the trade-off methods incorporating exploitation can perform at least as well, if not better than maximum variance. Thus, we discuss how the choice of the utility function depends on the distribution of the data, the model performance and uncertainties, additive noise as well as the budget.

We present Cephalo, a series of multimodal vision large language models (V-LLMs) designed for materials science applications, integrating visual and linguistic data for enhanced understanding and interaction within human-AI and multi-agent AI frameworks. A key innovation of Cephalo is its advanced dataset generation method, which employs a sophisticated algorithm to accurately detect and separate images and their corresponding textual descriptions from PDF documents, such as scientific papers. The method includes a careful refinement of image-text pairs through integrated vision and language processing, ensuring high-quality, contextually relevant, and well reasoned training data. Cephalo is trained on integrated image and text data extracted from thousands of scientific papers and science-focused Wikipedia pages demonstrates can interpret complex visual scenes, generate precise language descriptions, and answer queries about images effectively. The combination of a vision encoder with an autoregressive transformer supports complex natural language understanding in an integrated model, which can be coupled with other generative methods to create an image-to-text-to-image or image-to-text-to-3D pipeline. To explore the development of larger models from smaller ones, we merge sets of layers that originate from different pre-trained source models. This hybrid approach allows us to leverage the ___domain-specific expertise and general conversational capabilities to harness the strengths of multiple models. We examine the models in diverse use cases that incorporate biological materials, fracture and engineering analysis, protein biophysics, and bio-inspired design based on insect behavior. Generative applications include bio-inspired designs, including pollen-inspired architected materials, as well as the synthesis of bio-inspired material microstructures from a photograph of a solar eclipse.

This paper introduces an advanced Computational Analytical Micromechanics (CAM) framework for linear thermoelastic composites (CMs) with periodic microstructures. The approach is based on an exact new Additive General Integral Equation (AGIE), formulated for compactly supported loading conditions, such as body forces and localized thermal effects (for example laser heating). In addition, new general integral equations (GIEs) are established for arbitrary mechanical and thermal loading. A unified iterative scheme is developed for solving the static AGIEs, where the compact support of loading serves as a new fundamental training parameter. At the core of the methodology lies a generalized Representative Volume Element (RVE) concept that extends Hill classical definition of the RVE. Unlike conventional RVEs, this generalized RVE is not fixed geometrically but emerges naturally from the characteristic scale of localized loading, thereby reducing the analysis of an infinite periodic medium to a finite, data-driven ___domain. This formulation automatically filters out nonrepresentative subsets of effective parameters while eliminating boundary effects, edge artifacts, and finite-size sample dependencies. Furthermore, the AGIE-based CAM framework integrates seamlessly with machine learning (ML) and neural network (NN) architectures, supporting the development of accurate, physics-informed surrogate nonlocal operators.

Large language models (LLMs) have demonstrated rapid progress across a wide array of domains. Owing to the very large number of parameters and training data in LLMs, these models inherently encompass an expansive and comprehensive materials knowledge database, far exceeding the capabilities of individual researcher. Nonetheless, devising methods to harness the knowledge embedded within LLMs for the design and discovery of novel materials remains a formidable challenge. We introduce a general approach for addressing materials classification problems, which incorporates LLMs, prompt engineering, and deep learning. Utilizing a dataset of metallic glasses as a case study, our methodology achieved an improvement of up to 463% in prediction accuracy compared to conventional classification models. These findings underscore the potential of leveraging textual knowledge generated by LLMs for materials especially in the common situation where datasets are sparse, thereby promoting innovation in materials discovery and design.

This study explores cardiovascular stents fabricated using laser powder bed fusion (LPBF); an emerging method to offer patient-specific customisable parts. Here, the shape memory alloy NiTi, in a near equiatomic composition, was investigated to deconvolve the material response from macroscopic component effects. Specifically, stress-geometry interactions were revealed, in-situ, for a minaturised cardiovascular stent subjected to an externally applied cylindrical stress whilst acquiring synchrotron X-ray imaging and diffraction data. The approach enabled the collection of spatially resolved micromechanical deformation data; the formation of stress-induced martensite and R-phase was evident, occurring in locations near junctions between stent ligaments where stress concentrations exist. In the as-fabricated condition, hardness maps were obtained through nanoindentation, demonstrating that the localised deformation and deformation patterning is further controlled by porosity and microstructural heterogeneity. Electron backscatter diffraction (EBSD) supported these observations, showing a finer grain structure near stent junctions with higher associated lattice curvature. These features, combined with stress concentrations when loaded will initiate localised phase transformations. If the stent was subjected to repeated loading, representing in-vivo conditions, these regions would be susceptible to cyclic damage through transformation memory loss, leading to premature component failure. This study highlights the challenges that must be addressed for the post-processing treatment of LABF-processed stents for healthcare-related applications.

A large transverse thermoelectric response, known as anomalous Nernst effect (ANE) has been recently observed in several topological magnets. Building a thermopile employing this effect has been the subject of several recent propositions. Here, we design and build a thermopile with an array of tilted adjacent crystals of Mn_3Sn. The design employs a single material and replaces pairs of P and N thermocouples of the traditional design with hermaphroditic legs. The design exploits the large lag angle between the applied field and the magnetization, which we attribute to the interruption of magnetic octupoles at the edge of xy-plane. Eliminating extrinsic contacts between legs will boost the efficiency, simplify the process and pave the way for a new generation of thermopiles.

We present CrystalDiT, a diffusion transformer for crystal structure generation that achieves state-of-the-art performance by challenging the trend of architectural complexity. Instead of intricate, multi-stream designs, CrystalDiT employs a unified transformer that imposes a powerful inductive bias: treating lattice and atomic properties as a single, interdependent system. Combined with a periodic table-based atomic representation and a balanced training strategy, our approach achieves 9.62% SUN (Stable, Unique, Novel) rate on MP-20, substantially outperforming recent methods including FlowMM (4.38%) and MatterGen (3.42%). Notably, CrystalDiT generates 63.28% unique and novel structures while maintaining comparable stability rates, demonstrating that architectural simplicity can be more effective than complexity for materials discovery. Our results suggest that in data-limited scientific domains, carefully designed simple architectures outperform sophisticated alternatives that are prone to overfitting.

This work addresses minimum-weight design of undamped Euler-Bernoulli frame structures under subresonant single-frequency harmonic excitations, focusing on (robust) dynamic compliance and (robust) peak input power with ellipsoidal load uncertainty. We develop a semidefinite reformulation of robust dynamic compliance for subresonant single-frequency excitation and prove its equivalence to robust peak input power. We show that both these response measures admit an exact reformulation as a free-vibration eigenvalue constraint with design-independent mass augmentation, unifying static, dynamic, and modal requirements. Despite the nonconvex polynomial dependence on cross-sectional areas, certified bounds on global minimizers are obtained via the moment-sum-of-squares hierarchy of semidefinite relaxations. Benchmark studies on 10- and 35-segment frames corroborate the theory. For the 10-segment problem, we obtain the global optimum; for the 35-segment frame, we find high-quality locally-optimal designs that substantially improve on the best known one. We further fabricate and experimentally validate an additional design that closely matches the predictions of the model.

Designing de novo proteins beyond those found in nature holds significant promise for advancements in both scientific and engineering applications. Current methodologies for protein design often rely on AI-based models, such as surrogate models that address end-to-end problems by linking protein structure to material properties or vice versa. However, these models frequently focus on specific material objectives or structural properties, limiting their flexibility when incorporating out-of-___domain knowledge into the design process or comprehensive data analysis is required. In this study, we introduce ProtAgents, a platform for de novo protein design based on Large Language Models (LLMs), where multiple AI agents with distinct capabilities collaboratively address complex tasks within a dynamic environment. The versatility in agent development allows for expertise in diverse domains, including knowledge retrieval, protein structure analysis, physics-based simulations, and results analysis. The dynamic collaboration between agents, empowered by LLMs, provides a versatile approach to tackling protein design and analysis problems, as demonstrated through diverse examples in this study. The problems of interest encompass designing new proteins, analyzing protein structures and obtaining new first-principles data -- natural vibrational frequencies -- via physics simulations. The concerted effort of the system allows for powerful automated and synergistic design of de novo proteins with targeted mechanical properties. The flexibility in designing the agents, on one hand, and their capacity in autonomous collaboration through the dynamic LLM-based multi-agent environment on the other hand, unleashes great potentials of LLMs in addressing multi-objective materials problems and opens up new avenues for autonomous materials discovery and design.

Self-supervised neural language models have recently achieved unprecedented success, from natural language processing to learning the languages of biological sequences and organic molecules. These models have demonstrated superior performance in the generation, structure classification, and functional predictions for proteins and molecules with learned representations. However, most of the masking-based pre-trained language models are not designed for generative design, and their black-box nature makes it difficult to interpret their design logic. Here we propose BLMM Crystal Transformer, a neural network based probabilistic generative model for generative and tinkering design of inorganic materials. Our model is built on the blank filling language model for text generation and has demonstrated unique advantages in learning the "materials grammars" together with high-quality generation, interpretability, and data efficiency. It can generate chemically valid materials compositions with as high as 89.7\% charge neutrality and 84.8\% balanced electronegativity, which are more than 4 and 8 times higher compared to a pseudo random sampling baseline. The probabilistic generation process of BLMM allows it to recommend tinkering operations based on learned materials chemistry and makes it useful for materials doping. Combined with the TCSP crysal structure prediction algorithm, We have applied our model to discover a set of new materials as validated using DFT calculations. Our work thus brings the unsupervised transformer language models based generative artificial intelligence to inorganic materials. A user-friendly web app has been developed for computational materials doping and can be accessed freely at www.materialsatlas.org/blmtinker.

Research and practice in Intelligent Design (ID) have significantly enhanced engineering innovation, efficiency, quality, and productivity over recent decades, fundamentally reshaping how engineering designers think, behave, and interact with design processes. The recent emergence of Foundation Models (FMs), particularly Large Language Models (LLMs), has demonstrated general knowledge-based reasoning capabilities, and open new paths and avenues for further transformation in engineering design. In this context, this paper introduces Intelligent Design 4.0 (ID 4.0) as an emerging paradigm empowered by agentic AI systems. We review the historical evolution of ID across four distinct stages: rule-based expert systems, task-specific machine learning models, large-scale foundation AI models, and the recent emerging paradigm of multi-agent collaboration. We propose a conceptual framework for ID 4.0 and discuss its potential to support end-to-end automation of engineering design processes through coordinated, autonomous multi-agent-based systems. Furthermore, we discuss future perspectives to enhance and fully realize ID 4.0's potential, including more complex design scenarios, more practical design implementations, novel agent coordination mechanisms, and autonomous design goal-setting with better human value alignment. In sum, these insights lay a foundation for advancing Intelligent Design toward greater adaptivity, autonomy, and effectiveness in addressing increasingly complex design challenges.

Generative machine learning (ML) models hold great promise for accelerating materials discovery through the inverse design of inorganic crystals, enabling an unprecedented exploration of chemical space. Yet, the lack of standardized evaluation frameworks makes it challenging to evaluate, compare, and further develop these ML models meaningfully. In this work, we introduce LeMat-GenBench, a unified benchmark for generative models of crystalline materials, supported by a set of evaluation metrics designed to better inform model development and downstream applications. We release both an open-source evaluation suite and a public leaderboard on Hugging Face, and benchmark 12 recent generative models. Results reveal that an increase in stability leads to a decrease in novelty and diversity on average, with no model excelling across all dimensions. Altogether, LeMat-GenBench establishes a reproducible and extensible foundation for fair model comparison and aims to guide the development of more reliable, discovery-oriented generative models for crystalline materials.

Native 3D generative models have achieved remarkable fidelity and speed, yet they suffer from a critical limitation: inability to prescribe precise structural articulations, where precise structural control within the native 3D space remains underexplored. This paper proposes SK-Adapter, a simple and yet highly efficient and effective framework that unlocks precise skeletal manipulation for native 3D generation. Moving beyond text or image prompts, which can be ambiguous for precise structure, we treat the 3D skeleton as a first-class control signal. SK-Adapter is a lightweight structural adapter network that encodes joint coordinates and topology into learnable tokens, which are injected into the frozen 3D generation backbone via cross-attention. This smart design allows the model to not only effectively "attend" to specific 3D structural constraints but also preserve its original generative priors. To bridge the data gap, we contribute Objaverse-TMS dataset, a large-scale dataset of 24k text-mesh-skeleton pairs. Extensive experiments confirm that our method achieves robust structural control while preserving the geometry and texture quality of the foundation model, significantly outperforming existing baselines. Furthermore, we extend this capability to local 3D editing, enabling the region specific editing of existing assets with skeletal guidance, which is unattainable by previous methods. Project Page: https://sk-adapter.github.io/

Within the paradigm of metamaterials and metasurfaces, electromagnetic properties of composite materials can be engineered by shaping or modulating their constituents, so-called meta-atoms. Synthesis and analysis of complex-shape meta-atoms with general polarization properties is a challenging task. In this paper, we demonstrate that the most general response can be conceptually decomposed into a set of basic, fundamental polarization phenomena, which enables immediate all-direction characterization of electromagnetic properties of arbitrary linear metamaterials and metasurfaces. The proposed platform of modular characterization (called "materiatronics") is tested on several examples of bianisotropic and nonreciprocal meta-atoms. As a demonstration of the potential of the modular analysis, we use it to design a single-layer metasurface of vanishing thickness with unitary circular dichroism. The analysis approach developed in this paper is supported by a ready-to-use computational code and can be further extended to meta-atoms engineered for other types of wave interactions, such as acoustics and mechanics.

The convergence of artificial intelligence and materials science presents a transformative opportunity, but achieving true acceleration in discovery requires moving beyond task-isolated, fine-tuned models toward agentic systems that plan, act, and learn across the full discovery loop. This survey advances a unique pipeline-centric view that spans from corpus curation and pretraining, through ___domain adaptation and instruction tuning, to goal-conditioned agents interfacing with simulation and experimental platforms. Unlike prior reviews, we treat the entire process as an end-to-end system to be optimized for tangible discovery outcomes rather than proxy benchmarks. This perspective allows us to trace how upstream design choices-such as data curation and training objectives-can be aligned with downstream experimental success through effective credit assignment. To bridge communities and establish a shared frame of reference, we first present an integrated lens that aligns terminology, evaluation, and workflow stages across AI and materials science. We then analyze the field through two focused lenses: From the AI perspective, the survey details LLM strengths in pattern recognition, predictive analytics, and natural language processing for literature mining, materials characterization, and property prediction; from the materials science perspective, it highlights applications in materials design, process optimization, and the acceleration of computational workflows via integration with external tools (e.g., DFT, robotic labs). Finally, we contrast passive, reactive approaches with agentic design, cataloging current contributions while motivating systems that pursue long-horizon goals with autonomy, memory, and tool use. This survey charts a practical roadmap towards autonomous, safety-aware LLM agents aimed at discovering novel and useful materials.

In recent years, diffusion-based models have demonstrated exceptional performance in searching for simultaneously stable, unique, and novel (S.U.N.) crystalline materials. However, most of these models don't have the ability to change the number of atoms in the crystal during the generation process, which limits the variability of model sampling trajectories. In this paper, we demonstrate the severity of this restriction and introduce a simple yet powerful technique, mirage infusion, which enables diffusion models to change the state of the atoms that make up the crystal from existent to non-existent (mirage) and vice versa. We show that this technique improves model quality by up to times2.5 compared to the same model without this modification. The resulting model, Mirage Atom Diffusion (MiAD), is an equivariant joint diffusion model for de novo crystal generation that is capable of altering the number of atoms during the generation process. MiAD achieves an 8.2% S.U.N. rate on the MP-20 dataset, which substantially exceeds existing state-of-the-art approaches. The source code can be found at https://github.com/andrey-okhotin/miad.git{github.com/andrey-okhotin/miad}.

Structural optimization is a popular method for designing objects such as bridge trusses, airplane wings, and optical devices. Unfortunately, the quality of solutions depends heavily on how the problem is parameterized. In this paper, we propose using the implicit bias over functions induced by neural networks to improve the parameterization of structural optimization. Rather than directly optimizing densities on a grid, we instead optimize the parameters of a neural network which outputs those densities. This reparameterization leads to different and often better solutions. On a selection of 116 structural optimization tasks, our approach produces the best design 50% more often than the best baseline method.

Materials synthesis is vital for innovations such as energy storage, catalysis, electronics, and biomedical devices. Yet, the process relies heavily on empirical, trial-and-error methods guided by expert intuition. Our work aims to support the materials science community by providing a practical, data-driven resource. We have curated a comprehensive dataset of 17K expert-verified synthesis recipes from open-access literature, which forms the basis of our newly developed benchmark, AlchemyBench. AlchemyBench offers an end-to-end framework that supports research in large language models applied to synthesis prediction. It encompasses key tasks, including raw materials and equipment prediction, synthesis procedure generation, and characterization outcome forecasting. We propose an LLM-as-a-Judge framework that leverages large language models for automated evaluation, demonstrating strong statistical agreement with expert assessments. Overall, our contributions offer a supportive foundation for exploring the capabilities of LLMs in predicting and guiding materials synthesis, ultimately paving the way for more efficient experimental design and accelerated innovation in materials science.

In this paper, we propose the MultiLevel Variational MultiScale (ML-VMS) method, a novel approach that seamlessly integrates a multilevel mesh strategy into the Variational Multiscale (VMS) framework. A key feature of the ML-VMS method is the use of the Convolutional Hierarchical Deep Neural Network (C-HiDeNN) as the approximation basis. The framework employs a coarse mesh throughout the ___domain, with localized fine meshes placed only in subdomains of high interest, such as those surrounding a source. Solutions at different resolutions are robustly coupled through the variational weak form and interface conditions. Compared to existing multilevel methods, ML-VMS (1) can couple an arbitrary number of mesh levels across different scales using variational multiscale framework; (2) allows approximating functions with arbitrary orders with linear finite element mesh due to the C-HiDeNN basis; (3) is supported by a rigorous theoretical error analysis; (4) features several tunable hyperparameters (e.g., order p, patch size s) with a systematic guide for their selection. We first show the theoretical error estimates of ML-VMS. Then through numerical examples, we demonstrate that ML-VMS with the C-HiDeNN takes less computational time than the FEM basis given comparable accuracy. Furthermore, we incorporate a space-time reduced-order model (ROM) based on C-HiDeNN-Tensor Decomposition (TD) into the ML-VMS framework. For a large-scale single-track laser powder bed fusion (LPBF) transient heat transfer problem that is equivalent to a full-order finite element model with 10^{10} spatial degrees of freedom (DoFs), our 3-level ML-VMS C-HiDeNN-TD achieves an approximately 5,000x speedup on a single CPU over a single-level linear FEM-TD ROM.

Recently, Large Language Models (LLMs) have achieved significant success, prompting increased interest in expanding their generative capabilities beyond general text into ___domain-specific areas. This study investigates the generation of parametric sequences for computer-aided design (CAD) models using LLMs. This endeavor represents an initial step towards creating parametric 3D shapes with LLMs, as CAD model parameters directly correlate with shapes in three-dimensional space. Despite the formidable generative capacities of LLMs, this task remains challenging, as these models neither encounter parametric sequences during their pretraining phase nor possess direct awareness of 3D structures. To address this, we present CAD-Llama, a framework designed to enhance pretrained LLMs for generating parametric 3D CAD models. Specifically, we develop a hierarchical annotation pipeline and a code-like format to translate parametric 3D CAD command sequences into Structured Parametric CAD Code (SPCC), incorporating hierarchical semantic descriptions. Furthermore, we propose an adaptive pretraining approach utilizing SPCC, followed by an instruction tuning process aligned with CAD-specific guidelines. This methodology aims to equip LLMs with the spatial knowledge inherent in parametric sequences. Experimental results demonstrate that our framework significantly outperforms prior autoregressive methods and existing LLM baselines.

Discovering novel materials is critical for technological advancements such as solar cells, batteries, and carbon capture. However, the development of new materials is constrained by a slow and expensive trial-and-error process. To accelerate this pipeline, we introduce PLaID++, a Large Language Model (LLM) fine-tuned for stable and property-guided crystal generation. We fine-tune Qwen-2.5 7B to generate crystal structures using a novel Wyckoff-based text representation. We show that generation can be effectively guided with a reinforcement learning technique based on Direct Preference Optimization (DPO), with sampled structures categorized by their stability, novelty, and space group. By encoding symmetry constraints directly into text and guiding model outputs towards desirable chemical space, PLaID++ generates structures that are thermodynamically stable, unique, and novel at a sim50\% greater rate than prior methods and conditionally generates structures with desired space group properties. Our experiments highlight the effectiveness of iterative DPO, achieving sim115\% and sim50\% improvements in unconditional and space group conditioned generation, respectively, compared to fine-tuning alone. Our work demonstrates the potential of adapting post-training techniques from natural language processing to materials design, paving the way for targeted and efficient discovery of novel materials.

Research in AI4Science has shown promise in many science applications, including polymer design. However, current LLMs prove ineffective on this problem space because: (i) most models lack polymer-specific knowledge (ii) existing aligned models lack coverage of knowledge and capabilities relevant to polymer design. Addressing this, we introduce PolyBench, a large scale training and test benchmark dataset of more than 125K polymer design related tasks, leveraging a knowledge base of 13M+ data points obtained from experimental and synthetic sources to ensure broad coverage of polymers and their properties. For effective alignment using PolyBench, we introduce a knowledge-augmented reasoning distillation method that augments this dataset with structured CoT. Furthermore, tasks in PolyBench are organized from simple to complex analytical reasoning problems, enabling generalization tests and diagnostic probes across the problem space. Experiments show that small language models (SLMs), of 7B to 14B parameters, trained on PolyBench data outperform similar sized models, and even closed source frontier LLMs on PolyBench test dataset while demonstrating gains on other polymer benchmarks as well.

Synthesis procedures play a critical role in materials research, as they directly affect material properties. With data-driven approaches increasingly accelerating materials discovery, there is growing interest in extracting synthesis procedures from scientific literature as structured data. However, existing studies often rely on rigid, ___domain-specific schemas with predefined fields for structuring synthesis procedures or assume that synthesis procedures are linear sequences of operations, which limits their ability to capture the structural complexity of real-world procedures. To address these limitations, we adopt PROV-DM, an international standard for provenance information, which supports flexible, graph-based modeling of procedures. We present MatPROV, a dataset of PROV-DM-compliant synthesis procedures extracted from scientific literature using large language models. MatPROV captures structural complexities and causal relationships among materials, operations, and conditions through visually intuitive directed graphs. This representation enables machine-interpretable synthesis knowledge, opening opportunities for future research such as automated synthesis planning and optimization.

Generative models trained on internet-scale data are capable of generating novel and realistic texts, images, and videos. A natural next question is whether these models can advance science, for example by generating novel stable materials. Traditionally, models with explicit structures (e.g., graphs) have been used in modeling structural relationships in scientific data (e.g., atoms and bonds in crystals), but generating structures can be difficult to scale to large and complex systems. Another challenge in generating materials is the mismatch between standard generative modeling metrics and downstream applications. For instance, common metrics such as the reconstruction error do not correlate well with the downstream goal of discovering stable materials. In this work, we tackle the scalability challenge by developing a unified crystal representation that can represent any crystal structure (UniMat), followed by training a diffusion probabilistic model on these UniMat representations. Our empirical results suggest that despite the lack of explicit structure modeling, UniMat can generate high fidelity crystal structures from larger and more complex chemical systems, outperforming previous graph-based approaches under various generative modeling metrics. To better connect the generation quality of materials to downstream applications, such as discovering novel stable materials, we propose additional metrics for evaluating generative models of materials, including per-composition formation energy and stability with respect to convex hulls through decomposition energy from Density Function Theory (DFT). Lastly, we show that conditional generation with UniMat can scale to previously established crystal datasets with up to millions of crystals structures, outperforming random structure search (the current leading method for structure discovery) in discovering new stable materials.

We present a learning-based system for rapid mass-scale material synthesis that is useful for novice and expert users alike. The user preferences are learned via Gaussian Process Regression and can be easily sampled for new recommendations. Typically, each recommendation takes 40-60 seconds to render with global illumination, which makes this process impracticable for real-world workflows. Our neural network eliminates this bottleneck by providing high-quality image predictions in real time, after which it is possible to pick the desired materials from a gallery and assign them to a scene in an intuitive manner. Workflow timings against Disney's "principled" shader reveal that our system scales well with the number of sought materials, thus empowering even novice users to generate hundreds of high-quality material models without any expertise in material modeling. Similarly, expert users experience a significant decrease in the total modeling time when populating a scene with materials. Furthermore, our proposed solution also offers controllable recommendations and a novel latent space variant generation step to enable the real-time fine-tuning of materials without requiring any ___domain expertise.

Optical design is the process of configuring optical elements to precisely manipulate light for high-fidelity imaging. It is inherently a highly non-convex optimization problem that relies heavily on human heuristic expertise and ___domain-specific knowledge. While Large Language Models (LLMs) possess extensive optical knowledge, their capabilities in leveraging the knowledge in designing lens system remain significantly constrained. This work represents the first attempt to employ LLMs in the field of optical design. We bridge the expertise gap by enabling users without formal optical training to successfully develop functional lens systems. Concretely, we curate a comprehensive dataset, named OptiDesignQA, which encompasses both classical lens systems sourced from standard optical textbooks and novel configurations generated by automated design algorithms for training and evaluation. Furthermore, we inject ___domain-specific optical expertise into the LLM through a hybrid objective of full-system synthesis and lens completion. To align the model with optical principles, we employ Group Relative Policy Optimization Done Right (DrGRPO) guided by Optical Lexicographic Reward for physics-driven policy alignment. This reward system incorporates structural format rewards, physical feasibility rewards, light-manipulation accuracy, and LLM-based heuristics. Finally, our model integrates with specialized optical optimization routines for end-to-end fine-tuning and precision refinement. We benchmark our proposed method against both traditional optimization-based automated design algorithms and LLM counterparts, and experimental results show the superiority of our method.

We introduce StableMaterials, a novel approach for generating photorealistic physical-based rendering (PBR) materials that integrate semi-supervised learning with Latent Diffusion Models (LDMs). Our method employs adversarial training to distill knowledge from existing large-scale image generation models, minimizing the reliance on annotated data and enhancing the diversity in generation. This distillation approach aligns the distribution of the generated materials with that of image textures from an SDXL model, enabling the generation of novel materials that are not present in the initial training dataset. Furthermore, we employ a diffusion-based refiner model to improve the visual quality of the samples and achieve high-resolution generation. Finally, we distill a latent consistency model for fast generation in just four steps and propose a new tileability technique that removes visual artifacts typically associated with fewer diffusion steps. We detail the architecture and training process of StableMaterials, the integration of semi-supervised training within existing LDM frameworks and show the advantages of our approach. Comparative evaluations with state-of-the-art methods show the effectiveness of StableMaterials, highlighting its potential applications in computer graphics and beyond. StableMaterials is publicly available at https://gvecchio.com/stablematerials.

Networks of atom-centered coordination octahedra commonly occur in inorganic and hybrid solid-state materials. Characterizing their spatial arrangements and characteristics is crucial for relating structures to properties for many materials families. The traditional method using case-by-case inspection becomes prohibitive for discovering trends and similarities in large datasets. Here, we operationalize chemical intuition to automate the geometric parsing, quantification, and classification of coordination octahedral networks. We find axis-resolved tilting trends in ABO_{3} perovskite polymorphs, which assist in detecting oxidation state changes. Moreover, we develop a scale-invariant encoding scheme to represent these networks, which, combined with human-assisted unsupervised machine learning, allows us to taxonomize the inorganic framework polytypes in hybrid iodoplumbates (A_xPb_yI_z). Consequently, we uncover a violation of Pauling's third rule and the design principles underpinning their topological diversity. Our results offer a glimpse into the vast design space of atomic octahedral networks and inform high-throughput, targeted screening of specific structure types.

Unified generation of sequence and structure for scientific data (e.g., materials, molecules, proteins) is a critical task. Existing approaches primarily rely on either autoregressive sequence models or diffusion models, each offering distinct advantages and facing notable limitations. Autoregressive models, such as GPT, Llama, and Phi-4, have demonstrated remarkable success in natural language generation and have been extended to multimodal tasks (e.g., image, video, and audio) using advanced encoders like VQ-VAE to represent complex modalities as discrete sequences. However, their direct application to scientific domains is challenging due to the high precision requirements and the diverse nature of scientific data. On the other hand, diffusion models excel at generating high-dimensional scientific data, such as protein, molecule, and material structures, with remarkable accuracy. Yet, their inability to effectively model sequences limits their potential as general-purpose multimodal foundation models. To address these challenges, we propose UniGenX, a unified framework that combines autoregressive next-token prediction with conditional diffusion models. This integration leverages the strengths of autoregressive models to ease the training of conditional diffusion models, while diffusion-based generative heads enhance the precision of autoregressive predictions. We validate the effectiveness of UniGenX on material and small molecule generation tasks, achieving a significant leap in state-of-the-art performance for material crystal structure prediction and establishing new state-of-the-art results for small molecule structure prediction, de novo design, and conditional generation. Notably, UniGenX demonstrates significant improvements, especially in handling long sequences for complex structures, showcasing its efficacy as a versatile tool for scientific data generation.

Inverse design refers to the problem of optimizing the input of an objective function in order to enact a target outcome. For many real-world engineering problems, the objective function takes the form of a simulator that predicts how the system state will evolve over time, and the design challenge is to optimize the initial conditions that lead to a target outcome. Recent developments in learned simulation have shown that graph neural networks (GNNs) can be used for accurate, efficient, differentiable estimation of simulator dynamics, and support high-quality design optimization with gradient- or sampling-based optimization procedures. However, optimizing designs from scratch requires many expensive model queries, and these procedures exhibit basic failures on either non-convex or high-dimensional problems.In this work, we show how denoising diffusion models (DDMs) can be used to solve inverse design problems efficiently and propose a particle sampling algorithm for further improving their efficiency. We perform experiments on a number of fluid dynamics design challenges, and find that our approach substantially reduces the number of calls to the simulator compared to standard techniques.

The generation of plausible crystal structures is often the first step in predicting the structure and properties of a material from its chemical composition. Quickly generating and predicting inorganic crystal structures is important for the discovery of new materials, which can target applications such as energy or electronic devices. However, most current methods for crystal structure prediction are computationally expensive, slowing the pace of innovation. Seeding structure prediction algorithms with quality generated candidates can overcome a major bottleneck. Here, we introduce CrystaLLM, a methodology for the versatile generation of crystal structures, based on the autoregressive large language modeling (LLM) of the Crystallographic Information File (CIF) format. Trained on millions of CIF files, CrystaLLM focuses on modeling crystal structures through text. CrystaLLM can produce plausible crystal structures for a wide range of inorganic compounds unseen in training, as demonstrated by ab initio simulations. The integration with predictors of formation energy permits the use of a Monte Carlo Tree Search algorithm to improve the generation of meaningful structures. Our approach challenges conventional representations of crystals, and demonstrates the potential of LLMs for learning effective 'world models' of crystal chemistry, which will lead to accelerated discovery and innovation in materials science.

The rise of Large Language Models (LLMs) has streamlined frontend interface creation through tools like Vercel's V0, yet surfaced challenges in design quality (e.g., accessibility, and usability). Current solutions, often limited by their focus, generalisability, or data dependency, fall short in addressing these complexities. Moreover, none of them examine the quality of LLM-generated UI design. In this work, we introduce DesignRepair, a novel dual-stream design guideline-aware system to examine and repair the UI design quality issues from both code aspect and rendered page aspect. We utilised the mature and popular Material Design as our knowledge base to guide this process. Specifically, we first constructed a comprehensive knowledge base encoding Google's Material Design principles into low-level component knowledge base and high-level system design knowledge base. After that, DesignRepair employs a LLM for the extraction of key components and utilizes the Playwright tool for precise page analysis, aligning these with the established knowledge bases. Finally, we integrate Retrieval-Augmented Generation with state-of-the-art LLMs like GPT-4 to holistically refine and repair frontend code through a strategic divide and conquer approach. Our extensive evaluations validated the efficacy and utility of our approach, demonstrating significant enhancements in adherence to design guidelines, accessibility, and user experience metrics.

The current advances in generative AI for learning large neural network models with the capability to produce essays, images, music and even 3D assets from text prompts create opportunities for a manifold of disciplines. In the present paper, we study the potential of deep text-to-3D models in the engineering ___domain, with focus on the chances and challenges when integrating and interacting with 3D assets in computational simulation-based design optimization. In contrast to traditional design optimization of 3D geometries that often searches for the optimum designs using numerical representations, such as B-Spline surface or deformation parameters in vehicle aerodynamic optimization, natural language challenges the optimization framework by requiring a different interpretation of variation operators while at the same time may ease and motivate the human user interaction. Here, we propose and realize a fully automated evolutionary design optimization framework using Shap-E, a recently published text-to-3D asset network by OpenAI, in the context of aerodynamic vehicle optimization. For representing text prompts in the evolutionary optimization, we evaluate (a) a bag-of-words approach based on prompt templates and Wordnet samples, and (b) a tokenisation approach based on prompt templates and the byte pair encoding method from GPT4. Our main findings from the optimizations indicate that, first, it is important to ensure that the designs generated from prompts are within the object class of application, i.e. diverse and novel designs need to be realistic, and, second, that more research is required to develop methods where the strength of text prompt variations and the resulting variations of the 3D designs share causal relations to some degree to improve the optimization.

Multiscale problems are ubiquitous in physics. Numerical simulations of such problems by solving partial differential equations (PDEs) at high resolution are computationally too expensive for many-query scenarios, e.g., uncertainty quantification, remeshing applications, topology optimization, and so forth. This limitation has motivated the application of data-driven surrogate models, where the microscale computations are substituted with a surrogate, usually acting as a black-box mapping between macroscale quantities. These models offer significant speedups but struggle with incorporating microscale physical constraints, such as the balance of linear momentum and constitutive models. In this contribution, we propose Equilibrium Neural Operator (EquiNO) as a complementary physics-informed PDE surrogate for predicting microscale physics and compare it with variational physics-informed neural and operator networks. Our framework, applicable to the so-called multiscale FE^{,2}, computations, introduces the FE-OL approach by integrating the finite element (FE) method with operator learning (OL). We apply the proposed FE-OL approach to quasi-static problems of solid mechanics. The results demonstrate that FE-OL can yield accurate solutions even when confronted with a restricted dataset during model development. Our results show that EquiNO achieves speedup factors exceeding 8000-fold compared to traditional methods and offers an optimal balance between data-driven and physics-based strategies.

Engineering Design is undergoing a transformative shift with the advent of AI, marking a new era in how we approach product, system, and service planning. Large language models have demonstrated impressive capabilities in enabling this shift. Yet, with text as their only input modality, they cannot leverage the large body of visual artifacts that engineers have used for centuries and are accustomed to. This gap is addressed with the release of multimodal vision language models, such as GPT-4V, enabling AI to impact many more types of tasks. In light of these advancements, this paper presents a comprehensive evaluation of GPT-4V, a vision language model, across a wide spectrum of engineering design tasks, categorized into four main areas: Conceptual Design, System-Level and Detailed Design, Manufacturing and Inspection, and Engineering Education Tasks. Our study assesses GPT-4V's capabilities in design tasks such as sketch similarity analysis, concept selection using Pugh Charts, material selection, engineering drawing analysis, CAD generation, topology optimization, design for additive and subtractive manufacturing, spatial reasoning challenges, and textbook problems. Through this structured evaluation, we not only explore GPT-4V's proficiency in handling complex design and manufacturing challenges but also identify its limitations in complex engineering design applications. Our research establishes a foundation for future assessments of vision language models, emphasizing their immense potential for innovating and enhancing the engineering design and manufacturing landscape. It also contributes a set of benchmark testing datasets, with more than 1000 queries, for ongoing advancements and applications in this field.