Predicting the thermodynamic properties of an alloy requires sampling its configurations across many chemical conditions and recovering free energies on a common absolute scale. Markov chain Monte Carlo (MCMC) is the standard tool, but it requires separate simulations at different conditions, and auxiliary free-energy methods such as thermodynamic integration are used to place results on a common absolute scale. Modern discrete neural samplers typically use reverse KL divergence as the objective and can be mode-seeking or biased. We present Free energy Offering Generative Sampler (FrOGS), a hybrid discrete neural sampler that couples an autoregressive model to a continuous-time Markov chain (CTMC) to be trained jointly under a single shared loss. FrOGS draws i.i.d. configurations, returns an unbiased estimate of the partition function, and gives consistent estimates of thermodynamic observables. We train a single model across a wide range of chemical conditions to produce estimates on a common absolute free-energy scale. FrOGS matches exact finite-size results on the 2D Ising model and reference phase diagrams for AgPd and CuAu, without mode collapse. We additionally compare to SEGAL, a published autoregressive baseline, and find that only FrOGS recovers the stability range of the CuAu$_3$ phase.
Estimating physical parameters from scientific images is a common inverse problem in materials characterization that often relies on expensive physics-based simulations. In electron microscopy, specimen thickness and crystal mistilt are critical parameters that govern how electrons scatter through the sample, and therefore the accuracy of any atomic-scale structure recovered from it. They are commonly inferred by matching experimental position-averaged convergent-beam electron diffraction (PACBED) patterns to simulated ones, but grid searches scale poorly and neural-network methods require extensive pretraining that may not transfer to new conditions. Here, we propose scalable Bayesian optimization of composite functions (SBOCF), a simulation-efficient method that exploits the known composite structure of the image-matching objective and the intermediate information contained in simulated images. By representing PACBED images with patch-level summaries and two correction terms, SBOCF preserves the original pixel-wise objective while reducing the number of modeled outputs from 24,649 to 11. Under a budget of 50 simulator evaluations, SBOCF outperformed standard Bayesian optimization with expected improvement on synthetic SrTiO3 benchmarks with thick and thin specimens, reducing the median final SSE by up to 290 times in the thick-sample case. On experimental data, SBOCF produced parameter estimates consistent with previously reported values without task-specific pretraining. For a simulated mistilted specimen, using the SBOCF estimates in a downstream ptychographic reconstruction recovered sharp atoms that were otherwise blurred. These results establish SBOCF as a promising approach for inverse problems involving expensive simulators and high-dimensional structured outputs.
The search for new crystalline materials spans an enormous compositional and structural space. Generating candidates in this space requires modeling the relationships between elemental composition, crystallographic symmetry, and crystal geometry. The space group specifies the crystal's symmetry and determines the admissible Wyckoff positions and geometric degrees of freedom; fixing it in advance prevents this global symmetry choice from being revised using information from evolving Wyckoff occupations and elemental composition. We introduce DynaCrys, the first framework for complete crystal generation in which the space group co-evolves with Wyckoff occupations and elements. We develop physics-informed space-group diffusion that explicitly incorporates crystallographic group-subgroup relations, and a legality-constrained stochastic decoder that jointly samples compatible space groups, Wyckoff occupations, and elements, followed by symmetry-constrained geometry generation. In large-scale evaluations on standard benchmarks, DynaCrys achieves state-of-the-art performance in symmetry-aware crystal generation while supporting fast sampling.
Accurate prediction of electronic Hamiltonians would enable broad property inference while avoiding the high computational cost of Density Functional Theory (DFT). However, progress toward general-purpose materials foundation models is limited by a data bottleneck: existing Hamiltonian datasets are typically small, lack structural diversity, and often omit essential relativistic physics such as spin--orbit coupling (SOC). We therefore construct UniHam, a large-scale Hamiltonian dataset and benchmark suite comprising 100,000+ DFT-computed complex-valued Hermitian Hamiltonians with full SOC, covering 72 elements and a wide range of crystal geometries and symmetries (spanning diverse lattice types and space-group families). Building on UniHam, we benchmark two representative state-of-the-art models under a standardized protocol and introduce complementary evaluation metrics that jointly assess three dimensions: (i) Hamiltonian reconstruction accuracy, (ii) out-of-distribution (OOD) generalization across composition/symmetry shifts, and (iii) the ability to support downstream property prediction from the predicted Hamiltonians. Experiments on UniHam demonstrate that the proposed benchmark and metrics effectively differentiate model capabilities, revealing intrinsic SOC- and element-dependent failure modes, large variations in compositional OOD robustness, and the necessity of spectral-level evaluation to assess whether Hamiltonian predictions reliably support downstream electronic-structure properties. Overall, UniHam provides a reproducible, SOC-complete benchmark that can sharpen model comparisons and accelerate the development of next-generation foundation models for quantum materials.
Large language models and the multi-agent systems built around them could accelerate materials discovery by connecting scientific knowledge with experimental decisions. Existing benchmarks establish capabilities in domain knowledge, multimodal interpretation and scientific tool use. As language models increasingly support materials research workflows, their ability to distinguish closely related material states and reason accurately with quantitative evidence remains insufficiently evaluated. These abilities are essential for comparing material responses, assessing mechanisms and maintaining reliable judgements as experimental evidence accumulates. We introduce MatScope to evaluate three connected capabilities. M1 tests unaided, condition-specific reasoning through 200 tasks spanning ten research functions, using aluminium and high-entropy alloys as representative material systems. M2 tests agent-assisted transfer of related knowledge to unresolved materials questions. MatEvoBench-20 tests initial forecasts across scientific dependency chains and revisions of still-hidden responses as observations accumulate. Across eleven model deployments, including GPT-6 Astra and Claude Fable 5.1, given-input calculations and many physical explanations are handled well. Fine-grained response estimates, comparisons between similar states and quantitatively supported choices remain substantially weaker. Related literature improves selected estimates, while condition and baseline mismatches limit transfer. Progressive observations calibrate some downstream responses and destabilize earlier accurate predictions. MatScope establishes measurable targets for developing reliable scientific reasoning in future self-evolving materials laboratories and materials-aware world models.
We study the learning of homogenized constitutive laws for inelastic heterogeneous materials, aiming to replace costly concurrent unit-cell simulations with surrogates that generalize across loading histories and microstructures. We focus on the recurrent neural operator framework, motivated by the explicit form of homogenized Kelvin--Voigt linear viscoelasticity. In this framework, internal variables enable a Markovian approximation of loading-history dependence, and neural operators represent the microstructure-dependent constitutive response. For periodic Kelvin--Voigt viscoelasticity, we prove a universal approximation theorem showing that the model can approximate the homogenized constitutive law to any prescribed accuracy, uniformly in time and over a wide set of admissible strain trajectories and microstructural property fields, in two and three dimensions. This comprises a significant extension of the existing, somewhat limited, one-dimensional theory that uses explicit solutions for piecewise constant materials. Instead, in two and three dimensions, we adopt a more versatile approximation based on the spectral representation of the memory kernel that arises from homogenization. This also enables us to give an explicit bound on the internal-variable dimension, sufficient for approximation, exhibiting logarithmic growth in the inverse relative stress error and in material contrast. Numerical experiments on viscoelasticity and crystal plasticity complement the theory, illustrating the roles of internal-variable dimension and sample complexity in learning homogenized responses from unit-cell data. Theoretical results are formally verified in Lean 4.
Universal machine-learned interatomic potentials could make excited-state simulations across chemical space routine, but excitation energies, unlike ground-state energies, are not sums of atomic contributions. The excited states of noninteracting molecules are the union of their states, which pooled multistate readouts reproduce at best for the lowest state. We introduce LEH-MACE, whose excitation energies are the eigenvalues of a local excitation Hamiltonian assembled from atom-centred blocks, so this union holds exactly. We generated TD-DFT energies and forces for about 300,000 equilibrium, thermal, and excited-state geometries of over 100,000 molecules. LEH-MACE's advantage over direct readouts grew with the distance from the training data and was largest above $S_1$, with about half their $S_2$ and $S_3$ errors for long conjugated oligomers. For molecule pairs, only LEH-MACE kept its single-molecule accuracy, while a softmin readout remained superior for $S_1$ dynamics of larger chromophores. Exact size consistency is thus one step toward such potentials.
Rapid, high-fidelity analysis of four-dimensional scanning transmission electron microscopy (4D-STEM) datasets from heterogeneous materials remains challenging because coexisting phases, orientation variants, local strain gradients, and intrinsic TEM thin-foil effects produce complex, overlapping diffraction signatures. Here, we present a machine-learning (ML) framework that combines physics-informed geometric descriptors with weighted high-dimensional embeddings to identify latent structural patterns with minimal prior knowledge. By constructing a regularized descriptor space before embedding and density-based clustering, the method improves cluster stability, suppresses noise-driven fragmentation, and reduces sensitivity to embedding hyperparameters. Spatial weighting produced the largest stability gain, increasing median cluster persistence from 0.04 to 0.55 while reducing the noise fraction from approximately 22% to 0%. Rotation weighting increased DBCV from 0.80 to 0.92, although the noise fraction rose from 0.2% to 1.0%, highlighting a trade-off between improved density separation and noise rejection. We validate the framework on two benchmark systems: Si/Si$_x$Ge$_{1-x}$ epitaxial layers with continuous lattice variation and deformation, and multiphase Ti-Nb alloys containing distinct phases and orientation variants. Comparisons with a pretrained vanilla autoencoder and model-free pattern vectorization show that the physics-informed geometric descriptor provides higher cluster fidelity, greater interpretability, and substantially lower dimensionality.
Large language models are increasingly deployed as autonomous agents for first-principles materials simulation. We report empirical findings from DFT-Agent Bench, a benchmark of 200+ Quantum ESPRESSO tasks spanning relaxation, electronic structure, equation-of-state, and elastic-tensor pipelines over multiple material tiers. Each task carries a QE-derived ground truth with public-reference cross-checks where available, and a provenance audit checks whether the required QE execution contract was met. Under one execution harness, we compare a near-bare ReAct baseline with a bundled v5.1 scaffold on two models. The complete scaffold improves bands+DOS by +0.08/+0.11 and d-electron vc-relax by +0.17 on both models, while high-scoring relaxation and equation-of-state cells leave little room for improvement. The elastic result is model-dependent (0.18 to 0.40 for deepseek-v4-pro and 0.62 to 0.59 for claude-opus-4-8). A fixed 100-task analysis with retrieval disabled supports the aggregate pattern: the fully frozen DeepSeek comparison gains +0.17, while the Opus comparison gains +0.10 against a historical pool baseline (p < 0.001). The provenance gate catches incomplete or unmarked executions that can receive high rubric scores; it is an execution-contract check, not a test for intentional fraud. These results characterize the evaluated DFT workflows. The anonymous review artifact contains the frozen diagnostic slice, prompts, scorer, and solver revisions: https://anonymous.4open.science/r/231e31re91287h/README.md.
Crystal Structure Prediction (CSP) aims to predict a material's 3D structure from its chemical composition, with applications from energy storage to biomedical devices. Despite its importance, existing evaluation frameworks suffer from key limitations: they rely on threshold-sensitive or incomparable metrics, focus predominantly on geometric performance while overlooking physical plausibility, and fail to account for polymorphism, where a chemical composition can crystallize into multiple stable structures. In parallel, recent Symmetry-Informed CSP (SICSP) methods often report results alongside standard CSP baselines while receiving crystallographic templates at inference, which constrain the search space and make SICSP a fundamentally different task. To address these limitations, we introduce an Orientation-invariant, Polymorph-Aware, Large Benchmark (OPAL-Bench) that evaluates CSP and SICSP as separate tasks. We evaluate 7 CSP and 2 SICSP methods under OPAL-Bench across 4 datasets using threshold-free geometric and physical distance metrics. Our results show that no method dominates across all metrics, and that geometric performance is not strongly correlated with physical plausibility. We also release OPAL-CSP, an SE(3)-equivariant flow-matching baseline for the CSP track that performs competitively on geometric metrics and ranks among the best on physical ones. By unifying geometric and physical metrics under a polymorph-aware protocol, OPAL-Bench enables a more comprehensive assessment of generative quality in CSP.
It is well established that molecular substructures can contribute unequally to chemical and physical properties, with specific motifs or side chains often playing dominant roles. Fragment-based representations have therefore emerged as an effective strategy for incorporating chemically meaningful inductive biases, as exemplified by molecular fingerprints and fragment-based attention mechanisms. However, many existing fragmentation-based machine learning methods rely on predefined chemical rules, which may yield suboptimal fragmentation for previously unseen or chemically unfamiliar structures and often overlook the importance of multiscale molecular representations. To address these limitations, we formulate molecular fragmentation as a radius-constrained optimization problem inspired by the k-center formulation, where the number of clusters is not fixed a priori but emerges from the specified radius, and propose a geometry-based fragmentation method that partitions arbitrary molecular or material structures using largely geometric information, without relying on predefined chemical fragmentation rules. The method provides flexible control over fragment size, enabling the construction of multiscale fragment representations for scale-adaptive modeling. Building on this framework, we develop a geometric fragment-based attention mechanism that integrates multiscale structural information and incorporate it into a multimodal machine learning model combining p-SMILES representations with three-dimensional (3D) conformational information. Experiments on a benchmark polymer dataset show that incorporating 3D conformational information improves prediction accuracy for several properties over models based exclusively on p-SMILES representations. Explainable artificial intelligence analyses further provide insights into the physical relevance of the learned representations.
Large databases of paper-derived experimental materials data hide essential information on materials. Their analysis is demanding, large-scale and complex, making manual knowledge extraction very difficult. To address this challenge, we developed Multi-Agentic AI (MAA) for automated, autonomous analysis of materials experimental big data and a specialized AI built on the obtained knowledge. MAA's nine role-specific AI agents, under predefined instructions and quality checks, autonomously perform data extraction, compositional feature generation, machine-learning modeling, feature-importance analysis and knowledge-base recording, iterating while inheriting previous knowledge. Delegating numerical processing to code makes large-scale data tractable; recording every choice and result enables later tracing to sources. In four thermoelectric-data experiments varying theme and cycle counts, the knowledge graph grew: knowledge clustered by theme and vocabulary was shared across themes. The specialized AI, searching and reading these records, answered materials questions citing sources. Retrospective verification also revealed errors, traced through the records to their sources.
Frequency-domain thermoreflectance (FDTR) is a laser pump-probe technique widely used to measure thermal properties at the micro- and nanoscale; however, it relies on a complex data analysis procedure that demands substantial domain expertise and is susceptible to subtle human errors. Here, we present Vibe-FDTR, an agent-oriented framework that enables large language model (LLM) agents to perform reliable and reproducible FDTR analyses directly from natural language requests. This framework couples a configuration-driven FDTR code package, which enforces physical and parametric consistency, with procedural agent skills that translate user intentions into organized and verifiable analysis steps. We evaluate Vibe-FDTR using a controlled benchmark with two levels: synthetic single-step tasks and real-data multi-step tasks based on measurements of gold-coated graphite samples. Across the two levels, agents using Vibe-FDTR achieve success rates of 100% and 98.9%, respectively. In sharp contrast, ablating skills (Code-agent) reduces performance to 91.4% and 36.7%, which drops further to 38.6% and 0% when the domain package is also omitted (Agent-only). Beyond success rate, Vibe-FDTR also reduces computational cost by 87.7% relative to the Code-agent variant and cuts execution time by more than 60%. Finally, an optional expert mode supports experimental planning via autonomous sensitivity and uncertainty evaluations, and formulates physically grounded recommendations for underspecified tasks. These results demonstrate that encapsulating domain code and expert knowledge into agent skills offers a promising route toward low-barrier, autonomous, and trustworthy thermal metrology.
Atomic properties such as partial charges or multipoles encode chemically meaningful information that can inform downstream molecular property prediction, but their evaluation as machine learning targets has been complicated by the absence of a principled out-of-distribution evaluation protocol at the atomic level. In this work, we propose a held-out evaluation protocol that clusters atomic environments by SOAP descriptors and computes metrics accounting only for cluster labels unseen during training. Following this procedure, we use 5$\times$5 cross-validation and Tukey's HSD to run a statistically rigorous comparison of E(3)-equivariant against non-equivariant, rotationally augmented models for predicting electron populations and multipoles of H, C, N, and O atoms. Building on our results, we introduce the Quantum Topological Neural Network (QT-Net), a rotationally augmented, non-equivariant graph neural network. We show that QT-Net can be used to infer properties of atoms in molecules from QM9 outside our training set, and that the atomic environments seen during training strongly affect the performance of molecular property prediction tasks. To further validate the framework, molecular dipole moments computed from QT-Net's per-atom outputs recover the ground-truth values reported in QM9. We release all code and data, including a JAX implementation of QT-Net.
Machine learning interatomic potentials (MLIPs) are commonly trained and evaluated by their ability to reproduce first-principles energies and forces. Practical value, however, is often determined by downstream processes such as structural relaxation. Much of MLIP literature is motivated by the expectation that improving force accuracy will produce correspondingly better downstream behavior. Although this expectation is natural, it may not hold in practice due to model inaccuracies. Here, we demonstrate that force accuracy and relaxation accuracy can be driven in opposite directions. Starting from pretrained MLIPs, we differentiate through relaxation trajectories and optimize the the final structures. This intervention produces increases in force-prediction errors while substantially reducing structural errors. Importantly, this represents a trade-off between two aspects of physical fidelity: the learned forces become less faithful to first-principles forces, while the resulting relaxed structures become more faithful to first-principles predictions. Rather than observing a discrepancy between local quality and downstream performance, we demonstrate that this discrepancy can be induced through optimization. Our findings suggest that MLIPs need not be optimized as approximations of first-principles forces, but can instead learn task-specific vector fields that guide relaxation trajectories toward more accurate final structures. By propagating supervision through complete relaxation trajectories, our framework captures dependencies between successive predictions that are absent when structure--force pairs are treated independently. More broadly, these results demonstrate that conventional force metrics can provide an incomplete assessment of downstream performance and highlights the importance of evaluating scientific machine-learning models within computational workflows.
Crystalline structure prediction is an essential prerequisite for designing materials with targeted properties. Yet, it is still an open challenge in materials design and drug discovery. Despite recent advances in computational materials science, accurately predicting three-dimensional non-polymeric crystal structures remains elusive. In this work, we focus on the molecular assembly problem, where a set~$\mathcal{S}$ of identical rigid molecules is packed to form a crystalline structure. Such a simplified formulation provides a useful approximation to the actual problem. However, while recent state-of-the-art methods have increasingly adopted sophisticated techniques, the underlying learning objective remains ill-posed. We propose a better formulation that introduces a loss function capturing key geometric molecular properties while ensuring permutation invariance over $\mathcal{S}$. Remarkably, we demonstrate that within this framework, a simple regression model already outperforms prior approaches, including flow matching techniques, on the COD-Cluster17 benchmark, a curated non-polymeric subset of the Crystallography Open Database (COD). Our code is available at https://github.com/inria-thoth/SinkFast.
The mechanical response of a crystal is governed by the evolving network of dislocations it contains, yet quantitatively linking the `state of that network' to its yield stress remains challenging. Here we represent the dislocation networks obtained from discrete dislocation dynamic simulation as graphs, using five distinct graph representations, characterize each network through a compact set of topological properties, and predict the yield stress from these graph properties and the applied strain rate using a standard random forest model evaluated with strain rate stratified cross-validation. The model predicts the yield stress with $R^2\approx0.86-0.90$ across all box sizes and $R^2\approx0.91-0.94$ for larger box sizes, and this accuracy is consistent across all five representations, indicating that the topology-stress relationship is a robust feature of the graph properties rather than an artefact of any single graph representation. We propose graph topology as a compact and robust route for connecting the microstructural state of a dislocation network to its mechanical response in addition to established variables.
This paper introduces AutoREC, an open-source Python platform for developing, training and evaluating reinforcement learning (RL) agents that automatically generate equivalent circuit models (ECMs) from electrochemical impedance spectroscopy (EIS) data. Although ECMs are widely used to interpret EIS measurements, their identification typically relies on manual trial-and-error, requiring domain expertise and limiting scalability, particularly in autonomous experimental pipelines such as self-driving laboratories. In AutoREC, ECM generation is formulated as a Markov decision process in which an RL agent sequentially modifies a circuit topology based on the current state, available actions and feedback from the resulting model. The platform supports an end-to-end workflow encompassing EIS preprocessing with selectable impedance representations, agent setup and training, ECM generation for new measurements and visualization-based evaluation and analysis of agent decision-making. AutoREC implements a configurable Double Deep Q-Network agent with prioritized experience replay and a dedicated deadloop mitigation strategy for navigating the complex circuit-generation action space efficiently. To demonstrate the platform, we trained a representative agent on 1350 synthetic spectra from five reference circuit families, evaluated it on 150 held-out synthetic spectra and applied it to 32 previously unseen experimental spectra from battery, corrosion, oxygen evolution reaction and CO2 reduction systems. These case studies illustrate the end-to-end capabilities of AutoREC while revealing challenges associated with experimental complexity and limited training-data coverage. The demonstrated agent serves as a reference implementation; AutoREC provides an extensible foundation through which users can develop and evaluate agents tailored to their specific electrochemical systems and research objectives.
Most existing equivariant architectures for Hamiltonian prediction propagate features in direct-sum spaces of irreducible spherical tensors, whereas the target Hamiltonian is naturally an operator block in a direct-product representation over local orbital and spin bases. This representation mismatch fragments contiguous Hamiltonian blocks, obscures direct manipulation of orbital couplings, and organizes features into irregular angular-momentum components that require numerous transformations and are poorly aligned with efficient hardware execution and memory management. To address both the representation mismatch and computational bottleneck, we propose DP-Learner, an equivariant learning framework that performs message passing directly on Hamiltonian-like operator blocks in the direct-product space. Theoretically, we propose Lie-generator-based directional embedding and invariantly weighted left--right products and contractions that preserve equivariance to SO(3), SU(2), and spatial inversions, without explicit Clebsch--Gordan decomposition or inverse reconstruction. Methodologically, we instantiate this principle as a Transformer architecture, in which Hamiltonian-like feature matrices or tensors evolve through equivariant operators in the direct-product space, while non-linear invariant scalar routing controls structured gating over matrix units, directional propagation, attention, and environment-embedded context interactions. We further construct MP-HAM-110K, a large-scale Hamiltonian dataset comprising more than 110,000 material structures covering 68 elements with both Hamiltonian and wavefunction data. Experiments on MP-HAM-110K and Materials-HAM-SOC demonstrate that DP-Learner dramatically improves Hamiltonian prediction accuracy and inference efficiency over the state-of-the-art method.
Symmetry governs the organization of physical structures, while symmetry breaking reveals their transformations. In geometric deep learning, symmetry imposes rank constraints on equivariant representations, limiting the expressive capacity of equivariant graph neural networks (GNNs). Here we show that these constraints can instead be exploited: the singular-value spectra of equivariant representations provide a unified fingerprint of structural symmetry. We introduce spectral symmetry fingerprints (SymFP), which enable discrete point-group identification through rank-template matching and continuous symmetry analysis by quantifying spectral energy beyond target rank constraints. SymFP is orientation invariant and architecture agnostic, enabling a parameter-free GNN implementation. Its spectra can be reused across multiple target groups, and the resulting leakage scores satisfy subgroup monotonicity. Across synthetic structures, molecules, coordination complexes and large biological assemblies, SymFP accurately identifies point groups, tracks controlled symmetry breaking and reveals local and degree-resolved symmetry changes that can be obscured by global geometric measures. These results establish the spectral structure of equivariant representations as a general framework for characterizing symmetry across physical systems.