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arXiv2026

Buckling Prediction for Nonlinear Elastic Beams with Soft Inclusions

We develop an efficient and accurate multiscale computational framework for predicting the buckling and post-buckling behaviour of elastic beams containing periodically distributed soft inclusions. The framework extends our previous multiscale, patch, computational homogenisation for linear elasticity by incorporating nonlinearity, and thus enables accurate prediction of both the buckling onset and the subsequent post-buckling response. Microscale computations are performed only within a sparse set of small subdomains (patches), while the macroscale behaviour is recovered through a proven patch-coupling algorithm. The scheme is assessed through quarter- and half-domain patch computations for beams with inclusion-to-matrix Young's modulus ratios ranging from 0.001 to 1. The results show that reducing the inclusion stiffness lowers both the critical buckling strain and the critical buckling stress, indicating an increased susceptibility to instability, while producing a milder post-buckling response with smaller transverse deflections and stress drops. Eigenvalue analysis of the Jacobian matrix accurately predicts the onset of instability and the corresponding critical strain and stress. Bifurcation diagrams of the nonlinear buckled configurations under compressive loading, and a quantitative analysis of the effect of the interpolation order on the predicted buckling and post-buckling responses, are also presented. Comparisons with full-domain simulations demonstrate that the proposed framework accurately predicts both the buckling threshold and the post-buckling behaviour while substantially reducing the computational cost. The methodology is readily extendable to heterogeneous beams, plates, shells, and other engineering structures.

math.NA↗

arXiv2026

HiPoly: a hierarchical polymer-native AI framework for property prediction and generative design

Polymeric materials are central to modern technologies, with applications ranging from energy to health and transportation. Although AI has made significant advances in materials discovery, the hierarchical structure of polymers across multiple length scales makes them inherently difficult to represent in a unified and physically meaningful way. Here we introduce HiPoly, a polymer-native AI framework that processes complete polymer descriptions through a three-level hierarchical graph architecture built on the G2RINS representation. HiPoly encodes stochastic inter-monomer connectivity, composition, and molecular weight directly within its architecture, using physically motivated design principles that mirror the multi-scale nature of polymeric systems. The framework establishes an end-to-end AI-driven workflow from experimental formulation data to property prediction, generative molecular design, and physics-based validation through molecular simulations, all unified by a single polymer representation. We demonstrate state-of-the-art prediction accuracy for thermophysical properties of multi-component polymer systems, with ablation studies confirming that each hierarchical design choice contributes independently to model performance. As an example, the generative design pathway is applied here to the discovery of sustainable alternatives to persistent fluorinated polymers, where it is possible to identify and independently validate PFAS-free candidates with target surface-energy properties. This work demonstrates how polymer-native AI can accelerate discovery by linking representation, prediction, and design across complex polymer chemistries.

physics.chem-ph↗

arXiv2026

Autonomous discovery of new structure-plausibility laws for explainable and rapid crystal diagnosis and screening

Crystal generators and tool-using agents propose structures faster than density functional theory (DFT) energy and phonon calculations or experiments can assess them. Deciding which candidates merit expensive assessment is therefore the bottleneck, yet most screens test little beyond atomic overlap and give no chemical reason for failure. Here, our agents generate, test and actively refute two million candidate laws, leaving eight Plausibility Rules for Inorganic Structures (PRIS). These laws encode five mechanisms: short-range repulsion, ionic contact and packing, electrostatic balance, bond-valence conservation and crystallographic site complexity. Experimental structures satisfy our law sets at 82--99%, but satisfy Pauling's rules 2--5 together at only 6.5%. The strictest set detects 87.9% of damaged crystal structures, whereas distance cutoffs detect only 1.6--3.2%. PRIS plausibility is linearly correlated with synthesizability, so the PRIS-derived synthesis score (PSS) explainably screens 83.7% of hard-to-synthesize structures while retaining 80.7% of experimental structures. In a property-conditioned inverse-design run, PRIS and PSS can reduce the DFT validation queue by up to 67.3% and keep 99.2% of the candidates whose DFT-validated bulk moduli reach the design target. Beyond screening, PRIS explains why GNoME remains enriched in rare low-symmetry structures and reveals how wrong-element assignments in falsified crystal reports hide behind plausible coordinates. PRIS moves screening from a pass-or-fail verdict to a chemical reason for failure, showing that autonomous agents can discover, by active refutation, physicochemical laws that guide calculations and experiments.

cond-mat.mtrl-sci↗

arXiv2026

Scalable Bayesian Optimization of Composite Functions for Image-Based Inverse Problems in Materials Characterization

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 290x 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.

cs.LG↗

arXiv2026

AutoREC: A reinforcement learning platform for equivalent circuit model generation

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 (DDQN) agent with prioritized experience replay and a dedicated dead-loop mitigation strategy for navigating the complex circuit-generation action space efficiently. To demonstrate the platform, we trained and evaluated a representative agent on synthetic EIS datasets and applied it to previously unseen experimental spectra from battery, corrosion, oxygen evolution reaction, and CO$_2$ 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.

cs.LG↗

arXiv2026

Evaluating a 4B open-weights local LLM for agentic DFT workflows: a literature reproducibility audit

Agentic workflows in materials science relying on hosted commercial models face severe reproducibility, economic, and data-privacy constraints. To explore fully local agentic science, this work evaluates an open-weights Qwen3:4B model executing an autonomous scientific pipeline across varying hardware constraints. Applied to pentagonal two-dimensional materials, the system extracts parameters from unstructured text, translates them into density functional theory (DFT) inputs, and drives simulations to convergence under a strict neurosymbolic architecture where agents propose and deterministic code disposes. The workflow is guarded by verbatim text grounding and multi-pass inference unions to counteract hardware-induced structural collapse. Evaluated against 201 expert judgements, the extractor achieves 95.7% precision (95% CI 90.3-98.1%) and 67.3% recall (59.8-74.0%), ensuring extracted parameters are strictly factual. However, precision identifying absent parameters does not exceed 47.0%, establishing that the measured omission rate constitutes a loose upper bound on true literature incompleteness. Across three hardware configurations, complete GPU residency governs extraction quality more fundamentally than weight or cache precision, raising Matthews correlation from 0.414 to 0.530 at fixed quantisation and to 0.560 with an unquantised cache. A corpus-scale audit indicates only 19 (33.3%) of the 57 studies are reproducible in principle, reporting every method parameter needed to re-initialise the calculation. Driven to convergence, the workflow reproduces published lattice constants with a mean absolute relative error of 2.3% where the relaxed structure retains its prototype, establishing that lightweight open-weights models can reliably drive autonomous agentic workflows when bounded by deterministic code gates.

cond-mat.mtrl-sci↗

arXiv2026

RAFT-DVC: Resolution-Aware Machine Learning-Based Digital Volume Correlation

Digital volume correlation (DVC) provides three-dimensional full-field displacement measurements from volumetric images, but how the internal resolution of a machine-learning-based DVC model affects accuracy and operating range remains poorly understood. Here, we present RAFT-DVC, a resolution-aware family of recurrent all-pairs field transforms (RAFT)-based DVC solvers with encoder downsampling factors s = 2, 4, and 8. Using a matched design, we find that the three solvers localize displacement to approximately 0.017 feature-grid voxel, giving an empirical raw-volume error scaling of approximately 0.017s voxel. The solvers exhibit complementary operating regimes governed jointly by displacement reach and volumetric-texture compatibility. Synthetic benchmarks show that RAFT-DVC achieves errors of the same order as tuned classical DVC under fine-texture, small-to-moderate-displacement conditions and becomes competitive or advantageous under coarse-texture, large-displacement conditions. Frequency-swept tests quantify deformation spatial resolution, while tiled inference enables dense estimation on large volumes. Evaluation on confocal volumetric images acquired during indentation illustrates the importance of matching solver operating regime to deformation magnitude and image texture. Tests on micro-CT images of elastomeric foam, despite training only on particle-labeled synthetic data, provide evidence of cross-texture transfer. We also identify coordinate-order inconsistencies in three-dimensional RAFT correlation sampling and introduce a non-cubic impulse test to verify sampler geometry independently of network training. Correcting the sampler improves native-input accuracy and generalization to unseen volume dimensions. Together, these results establish RAFT-DVC as a fast, resolution-aware framework for dense DVC with characterized accuracy and operating regimes.

cs.CV↗

arXiv2026

AutoXRD: Autonomous LLM Agents and Comprehensive Evaluation for Powder Diffraction Analysis

Powder X-ray diffraction (XRD) is central to materials characterization, yet reliable end-to-end automation remains challenging. An XRD agent must interpret diffraction evidence, operate refinement software, manage coupled parameters in a defensible order, and distinguish numerical improvement from physical validity. In this paper, we propose AutoXRD, an autonomous large language model (LLM) agent framework that organizes powder-XRD analysis as stepwise refinement, grounds actions in observed evidence, and applies deterministic crystallographic and physical checks before accepting results. We further introduce XRDBench with two complementary tracks. XRDBench-QA contains 100 bounded diagnostic tasks that isolate scientific reasoning and decision-making, whereas XRDBench-E2E contains 34 executable workflows that test whether agents can compose these capabilities into complete analyses requiring file inspection, crystallographic-software execution, iterative refinement, evidence preservation, and reporting. We evaluate ten recent LLMs across 1,340 model--task runs. Models average only 57.8 out of 100, falling from 61.9 on XRDBench-QA to 53.7 on XRDBench-E2E. They perform best on refinement-history assessment and result acceptance, but remain substantially weaker on refinement-action selection, phase quantification, indexing, and Rietveld refinement. GPT-5.6 Sol achieves the highest overall score of 81.1, GPT-5.6 Terra the highest XRDBench-E2E point estimate of 81.0, and GPT-5.6 Luna the best score--cost trade-off. Ablations show that all six AutoXRD components consistently improve performance, supporting the framework design. Finally, execution-trace analysis reveals recurring failures in coupled-parameter control, quantitative reasoning, evidence preservation, and workflow termination, motivating stronger scientific constraints, uncertainty-aware decisions, and more efficient planning.

cond-mat.mtrl-sci↗

arXiv2026

Can Coding Agents Reproduce Findings in Computational Materials Science?

Large language models are increasingly deployed as autonomous coding agents and have achieved remarkably strong performance on software engineering benchmarks. However, it is unclear whether such success transfers to computational scientific workflows, where tasks require not only strong coding ability, but also the ability to navigate complex, domain-specific procedures and to interpret results in the context of scientific claims. To address this question, we present AutoMat, a benchmark for evaluating LLM-based agents' ability to reproduce claims from computational materials science. AutoMat poses three interrelated challenges: recovering underspecified computational procedures, navigating specialized toolchains, and determining whether the resulting evidence supports a claim. By working closely with subject matter experts, we curate a set of claims from real materials science papers to test whether coding agents can recover and execute the end-to-end workflow needed to support (or undermine) such claims. We then evaluate multiple representative coding agent settings across several foundation models. Our results show that current LLM-based agents obtain low overall success rates on AutoMat, with the best-performing setting achieving a success rate of only 53%. Error analysis further reveals that agents perform worst when workflows must be reconstructed from paper text alone and that they fail primarily due to incomplete procedures, methodological deviations, and execution fragility. Taken together, these findings position AutoMat as both a benchmark for computational scientific reproducibility and a tool for diagnosing the current limitations of agentic systems in AI-for-science settings.

cs.CL↗

arXiv2026

Percolation Dynamics in Optimization : Variance Cascades and Discrete Scale Invariance

We study the dynamics of Stochastic Gradient Descent (SGD), which is known to steer deep neural networks toward invariant sets that correspond to simpler subnetworks. How this steering unfolds over time remains poorly understood. We answer this by modeling the stochastic gradient flow (SGF) as a percolation process, in which architectural symmetries force subnetworks to merge in discrete simultaneous blocks rather than one at a time. These structural transitions register as variance spikes in a macroscopic order parameter, echoing physical phase transitions. We further show this trapping mechanism and its associated scaling cascade extend to Adam and AdamW under an explicit heavy-tailed noise model.

cs.LG↗

arXiv2026

Coarse-Graining Hidden Representations: Unsupervised Neuron Selection via Mapping Entropy

Overparameterized neural networks carry far more hidden units than a task nominally requires, raising the question of which neurons are essential and whether that distinction is legible in the representation itself, without labels or gradients. We cast neuron selection as the problem of coarse-graining the hidden layer by retaining a subset of its neurons, and score each putative selection by the mapping entropy (ME). This quantity measures the loss of discriminatory power inherent in discarding part of the network neurons, and the selection that minimises the ME is taken as particularly informative. This criterion is fully unsupervised, in that it depends only on hidden-activation statistics. In teacher-student networks, ME optimisation recovers the minimal teacher-consistent representation and retains extra units in proportion to the hidden layer's residual variability; in a non-linear Gaussian process task, it selects coherent functional-class mappings whose preferred class shifts across training. On this task and on translation-augmented MNIST, ME-selected subnetworks outperform random subsets of equal size, most clearly under strong compression - linking configurational distinguishability to predictive performance.

cs.LG↗

arXiv2026

Data Driven Equation Discovery for Phase-Ordering Dynamics : From Allen Cahn to the Ising Model

Data-driven discovery of governing equations from spatiotemporal data offers a promising route to obtaining coarse-grained descriptions of complex dynamical systems. Here, we investigate the performance of PDE-SINDy for discovering phase-ordering dynamics using the Allen--Cahn equation as a benchmark and the Ising model with Glauber spin-flip dynamics as a microscopic system. We systematically analyze the effects of data availability, size of the candidate library, and noise on the efficiency of the equation discovery. We find that stability-selection PDE-SINDy can robustly identify the relevant terms in the governing dynamics even under limited or noisy data, while the recovered coefficient values are substantially more sensitive to these factors. We further show that enlarging the candidate library can strongly affect both term identification and coefficient recovery. Incorporating library bagging with stability selection reduces this sensitivity and improves the efficiency of equation discovery. For the Glauber spin flip Ising model dynamics, the resulting coarse-grained equation reproduces the characteristic phase-separation and coarsening dynamics of the underlying microscopic system. Overall, our results demonstrate the potential of PDE-SINDy for phase-ordering systems while highlighting the importance of carefully assessing the factors that influence the efficiency of equation discovery.

cond-mat.soft↗

arXiv2026

Physical policy gradient theorem for in situ stochastic-adjoint training

In situ adjoint training extracts parameter gradients directly from measurement, but has so far been limited to reciprocal or restricted systems. Here, we introduce the physical counterpart of the policy gradient theorem: a stochastic-adjoint gradient estimator that lifts these constraints by trading reciprocity for nondegenerate diffusion. As validation, we train a nonlinear resonator network, whose own dynamics supply the policy, against antagonistic temporal modulations with gradients from measured stochastic trajectories alone, without finite differences or a separate adjoint experiment.

physics.optics↗

arXiv2026

Quantum Circuit and Tensor Network Implementation of the 2D Acoustic Wave Equation

We present a cohesive framework for simulating seismic wave propagation utilizing quantum computing paradigms and their classical tensor network equivalents. We detail a quantum circuit-based formulation for the explicit finite-difference time-domain (FDTD) solution of the two-dimensional acoustic wave equation and map this quantum architecture onto a tensor train representation, namely for Matrix Product State (MPS). The MPS solver enables deterministic simulation of large-scale wavefield dynamics on classical high-performance computing systems. We demonstrate the MPS representation by computing 2D seismic wavefields on the Marmousi model. Our results indicate that the MPS representation is a viable direction for computing and scaling wavefield propagation.

quant-ph↗

arXiv2026

Shortcomings and capacities of real-constrained neural networks in complex spaces

We find the asymptotic ratio between the storage capacities when enforcing real pre-activations in a complex hypothesis class as opposed to complex ones in the same class. We use weights drawn from the complex Gaussian, which converge asymptotically in norm to the square root of dimension almost surely. Our methods depend on Gardner volume-type comparisons at critical capacity. Our proof relies on an application of the Harish-Chandra-Itzykson-Zuber (HCIZ) formula, nonstandard in literature. With the HCIZ formula, we may obtain a more robust approximation for the final asymptotic ratio. This strategy is applicable to our work specifically since we integrate over the unitary and orthogonal compact manifolds, facilitated via the Weyl integration formula and the Haar measure.

cs.LG↗

arXiv2026

On the Existence of Consistent Adversarial Attacks in High-Dimensional Linear Classification

What fundamentally distinguishes an adversarial attack from a misclassification due to limited model expressivity or finite data? In this work, we investigate this question in the setting of high-dimensional binary classification, where statistical effects due to limited data availability play a central role. We introduce a new error metric that precisely capture this distinction, quantifying model vulnerability to consistent adversarial attacks -- perturbations that preserve the ground-truth labels. Our main technical contribution is an exact and rigorous asymptotic characterization of these metrics in both well-specified models and latent space models, revealing different vulnerability patterns compared to standard robust error measures. The theoretical results demonstrate that as models become more overparameterized, their vulnerability to label-preserving perturbations grows, offering theoretical insight into the mechanisms underlying model sensitivity to adversarial attacks.

stat.ML↗

arXiv2026

The thermodynamic freedom of a thermodynamic computer

Thermodynamic computers are stochastic physical devices designed to perform calculations at the thermal energy scale. Their operation is constrained by the equations of stochastic thermodynamics, among which are a set of bounds, known as speed limits, that relate a thermodynamic computer's run time to its computational progress and the heat it dissipates. Using the Wasserstein speed limit we assess the thermodynamic efficiency of a simulation model of a thermodynamic computer trained to perform a standard machine-learning classification task. On this task the thermodynamic computer is as capable as a simple multilayer perceptron. We show that different inference protocols allow the computer to operate within 40\% of the thermodynamic limit of efficiency without loss of accuracy, or to perform inference increasingly rapidly at fixed accuracy and thermodynamic efficiency. These results indicate that a thermodynamic computer designed for a particular task retains considerable freedom in its thermodynamic operation.

cond-mat.stat-mech↗

arXiv2026

Breakdown of Edgeworth Expansion in Finite-Blocklength Regime and Exact Absorption via $q$-Deformation

This paper addresses the structural breakdown of the Edgeworth expansion in the finite-blocklength (FBL) regime, where conventional asymptotic approximations yield unphysical negative probabilities in the deep-tail region. We propose a $q$-deformed framework that resolves this inconsistency by replacing additive polynomial perturbations with a geometric deformation of the information density space. Motivated by the linearization of nonlinear dynamics, we prove that dynamically scaling the $q$-logarithmic parameter exactly absorbs the third-order skewness while preserving global nonnegativity. We establish a universal asymptotic matching, demonstrating that the framework encapsulates higher-order asymptotic scales. Numerical results confirm that the proposed method matches the state-of-the-art precision of the Cornish-Fisher bound without the risk of negative probabilities. The framework offers a robust and computationally stable foundation for evaluating operational limits in ultra-reliable communications such as 6G and URLLC.

cs.IT↗