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arXiv2026

Physics-informed learning for the inverse problem in resonant ultrasound spectroscopy

Inferring elastic constants from resonant ultrasound spectra is a nonlinear and typically overdetermined inverse problem based on finite spectral data. We formulate the Rayleigh-Ritz inverse problem as a constrained inverse-isospectral problem on the set of physically admissible elasticity tensors. This induces effective low-dimensional variables for the inverse map on the admissible elasticity manifold: length and elastic scales, aspect-ratio coordinates, scale-free spectral features, and stability-respecting elastic ratios. We use these variables to construct a physics-informed learning pipeline in which a regression model acts only on reduced spectral and geometric features, while scale recovery and final elastic-constant reconstruction are imposed analytically. For the full cubic benchmark, the reconstructed constants have MAE values of $20.37(35.15)$, $24.30(41.33)$, and $2.13(3.66)~\mathrm{GPa}$ for $C_{11}$, $C_{12}$, and $C_{44}$. In the fixed-geometry benchmark, the corresponding cubic MAPE values are $4.14(3.87)\%$, $8.31(8.50)\%$, and $2.44(2.86)\%$, while the isotropic values are $4.0(3.6)\%$ and $0.4(0.3)\%$ for the bulk and shear moduli. The inverse problem then becomes a constrained regression problem in variables adapted to the geometry, scaling, crystal symmetry, and thermodynamic stability of Hookean elasticity.

cond-mat.mtrl-sci↗
arXiv2026

Coordinate-Residual Physics-Driven Neural Network for Inverse Scattering Imaging

Electromagnetic inverse scattering is a nonlinear and ill-posed computational imaging problem, where accurate reconstruction is challenging due to measurement limitations, noise, and high computational costs, especially for 3-D imaging. Although physics-driven neural networks (PDNNs) reduce the dependence on labeled training data, existing accelerated PDNN frameworks often rely on preliminary reconstruction-based region selection, which may introduce instability when the selected region is inaccurate. In this paper, a coordinate-residual physics-driven neural network (CRPDNN) is proposed for 3-D electromagnetic inverse scattering. CRPDNN represents the unknown complex contrast distribution using normalized spatial coordinates and a residual convolutional network, whose parameters are optimized by enforcing consistency between the measured and model-predicted scattered fields. Unlike existing subregion-accelerated PDNN approaches, CRPDNN does not require a preliminary reconstruction, thereby avoiding dependence on its accuracy. For the reported noise-free 3-D synthetic cases, CRPDNN achieves an average relative error of 2.10\%, compared with 7.97\% for CSI and 3.99\% for $L_{2/3}$-FBE-WCIE, while providing approximately 5.5- and 12.1-fold speedups over the two baselines, respectively. Additional 2-D comparisons further demonstrate its stability and computational efficiency relative to existing PDNN frameworks. CRPDNN also maintains reliable reconstruction performance under noisy measurements, and the 3-D Fresnel experiments further indicate its potential for practical imaging applications.

physics.comp-ph↗
arXiv2026

Physics-Guided Concentration Inference from Resistance Transients in a Mixed-Phase SnO-SnO$_2$ Carbon Monoxide Sensor with p-n Switching

This work presents a physics-guided machine-learning framework for carbon monoxide concentration inference from experimentally measured resistance transients of a mixed-phase SnO-SnO$_2$ material gas sensor exhibiting temperature-dependent p-n switching behavior. Cycle-level transient responses are represented through physically interpretable descriptors and complemented by compact fast Fourier transform (FFT) and discrete wavelet transform (DWT)-based summaries. Using leakage-aware grouped cross-validation, we study both multi-class concentration classification and continuous concentration regression for the p-type and n-type sensing regimes separately. Across both regimes, fused features provide the strongest overall performance, while the physics-guided descriptor block remains highly competitive, indicating that the dominant concentration information is already encoded in physically meaningful transient dynamics. The p-type branch shows the best concentration-class discrimination, with the fused Random Forest classifier reaching approximately $96.5\%$ accuracy, whereas the n-type branch yields the best quantitative concentration estimation, with the fused Random Forest regressor achieving an MAE$\approx 1.48$ ppm and an R$^2$ $\approx 0.992$. These results reveal a clear dual-regime behavior: p-type sensing is particularly favorable for classification, whereas n-type sensing is more favorable for high-fidelity regression. More broadly, the study demonstrates that leakage-aware, cycle-level, physics-guided machine learning can extend conventional gas-sensing analysis beyond single-response metrics while preserving physical interpretability

physics.chem-ph↗
arXiv2026

Diffusion-Based Inverse Design of Dielectric Resonator Metasurfaces for Shaping Smart Electromagnetic Environments

Future wireless systems are expected to transform the surrounding space from a passive propagation medium into a smart electromagnetic environment, where engineered surfaces control wave propagation, support wireless sensing, and create programmable electromagnetic fingerprints. A key challenge in realizing this vision is the inverse design of metasurfaces for tailored electromagnetic propagation. While forward analysis evaluates the response of a known geometry, the inverse task starts from a prescribed scattering signature and seeks a physically realizable structure that produces it. This inverse task is inherently nonlinear and often high-dimensional, while candidate solutions may be non-unique and provide no direct indication of practical realizability. Here, we introduce a conditional diffusion framework for inverse design of dielectric resonator metasurfaces from target angular scattering patterns. Trained on T-matrix simulated geometry-response pairs, the model learns a conditional distribution of geometries instead of a deterministic mapping, enabling multiple candidate designs for the ill-posed inverse problem. The best generated metasurface achieves a mean percentage error of 1.39%, outperforming CMA-ES optimization (4.1% after 10 h) while requiring only about one minute for after-training inference. The model also produces lower error distributions than deterministic neural baselines for out-of-distribution spectra, highlighting the potential of diffusion models for efficient metasurface design.

cs.LG↗
arXiv2026

Beyond sensitivity: mechanism-resolved error budgets for designing quantum sensors

Quantum sensors are specified by a headline sensitivity, yet applications also demand accuracy and reliability. The dominant limiter of one metric is often known, but no method resolves how interacting mechanisms combine into a signed, per-mechanism budget for each metric. We introduce a framework that computes a sensor's sensitivity, accuracy, and robustness from one open-system simulation and attributes each to its limiting mechanism. For a nitrogen-vacancy diamond ensemble the attribution inverts across metrics: dephasing limits sensitivity, the thermal ground-state shift limits accuracy, and optical leakage limits robustness. At identical sensitivity the recovered-field bias spans $8$ to $1500$\,nT, so tuning to sensitivity alone can miss the accuracy target by two orders of magnitude. The same modeling transfers to a cesium optically pumped magnetometer recording a human magnetocardiogram. As a digital twin, it predicts the gain from addressing each limiter, so sensors can be designed to the required metrics.

quant-ph↗
arXiv2026

Arctic Dispersion Interruption Phenomenon and Sound Source Depth Estimation

The sound speed profile in the deep Arctic Ocean causes the surface layer to form a normal mode waveguide. When the depth of the sound source or receiver is near a node of the eigenfunction, the source cannot excite the mode, or the receiver cannot detect it, resulting in the modal amplitude at the receiver being approximately zero. This manifests as a dispersion interruption in the dispersion structure, which can be observed through time-frequency analysis of the received acoustic signal. Based on the interruption frequency identified from the received signal, combined with the relationship between node depth and modal frequency calculated from the ocean sound speed profile, the source depth can be estimated if the receiver depth is known. The phenomenon of dispersion interruption and the method of estimating source depth have been validated through simulations and experiments.

physics.app-ph↗
arXiv2026

Evaluating LLM-based AI agents integrated with materials synthesis tools: the case of atomic layer deposition

This work provides an overview of the different strategies that can be used to evaluate the performance of AI models and agents based on large language models (LLMs) for materials synthesis. After providing a brief overview of the key technologies behind the current generation of AI agents based on LLMs, we summarize the different approaches to evaluating these models in the context of materials science and in particular on materials synthesis, with a specific emphasis on scenarios in which the models are directly integrated with experimental tools. We discuss evaluation strategies spanning knowledge and reasoning benchmarks, tool-use benchmarks, and closed loop benchmarks involving the interaction with experimental systems or realistic virtual tools. We use atomic layer deposition (ALD) as a case study, emphasizing how existing approaches in the literature both build from general approaches used beyond materials science and can be generalized to other materials synthesis techniques. Finally, we provide a practical evaluation framework to evaluate LLMs in the context of materials synthesis

cond-mat.mtrl-sci↗
arXiv2026

A unified geometric design framework for kirigami structures

In recent years, kirigami metamaterials have been widely studied and applied in science and engineering. While various two- and three-dimensional kirigami design methods have been developed, most of them are only applicable to a limited class of kirigami structures. In this work, we develop a unified framework for kirigami design that encompasses a wide range of 2D-to-2D, 2D-to-3D, and 3D-to-3D shape-morphing effects, as well as additional geometric and physical properties such as compact reconfigurability and rigid deployability. In particular, by reformulating the design task as a length-based constrained optimization problem and solving it simultaneously for multiple target states of the kirigami structure, our unified design framework enables greater design flexibility and stronger theoretical support. Experimental results with a wide range of shape-morphing effects are presented to demonstrate the effectiveness of our framework. We further present a rigorous theoretical analysis of several key aspects of kirigami design, covering inertia transposition, aspect-ratio law, and angle defects, thereby elucidating important design rules and limitations. Altogether, our work paves a new way for the design of shape-morphing mechanical metamaterials.

cond-mat.soft↗
arXiv2026

Geometric integrators for adiabatically closed simple thermodynamic systems

A variational formulation for non-equilibrium thermodynamics was developed by Gay-Balmaz and Yoshimura. In a recent article, the first two authors of the present paper introduced partially cosymplectic structures as a geometric framework for thermodynamic systems, recovering the evolution equations obtained variationally. In this paper, we develop a discrete variational principle for adiabatically closed simple thermodynamic systems, which can be utilised to construct numerical integrators for the dynamics of such systems. The effectiveness of our method is illustrated with several examples.

math-ph↗
arXiv2026

Why Multi-Layer Message Passing Works: Completeness Theory for Graph Neural Network Interatomic Potentials

We prove that the Hypergraph Neural Network, an invariant architecture with 3-body message passing, is a universal approximator for potential energy surfaces. Our main contribution is a multi-layer completeness theory. We show that $L$ layers of message passing on sparse, cutoff-based graphs achieve the same representational power as having access to the full $L$-hop neighborhood, provided the configurations are generic, satisfy an overlap condition and a connectivity condition. This provides the first rigorous justification for the common practice of using multi-layer message passing with a per-layer cutoff smaller than the physical interaction range, the setting used by virtually all practical graph neural network based machine-learned interatomic potentials. As immediate consequences, we show that both DPA3 and CHGNet architectures inherit universal approximation.

cs.LG↗
arXiv2026

A brief history of quantum vs classical computational advantage

In this review article we summarize all experiments claiming quantum computational advantage to date. Our review highlights challenges, loopholes, and refutations appearing in subsequent work to provide a complete picture of the current statuses of these experiments. In addition, we also discuss theoretical computational advantage in example problems such as approximate optimization and recommendation systems. Finally, we review recent experiments in quantum error correction -- the biggest frontier to reach experimental quantum advantage in Shor's algorithm.

quant-ph↗
arXiv2026

Convergence and efficiency proof of quantum imaginary time evolution for bounded order systems

Many current and near-future applications of quantum computing utilise parametric families of quantum circuits and variational methods that can suffer from obstacles including non-convergence to the global minimum due to local minima, critical slowing down, or exponential resource scaling. Here we show that quantum imaginary time evolution can overcome these obstacles if the underlying physical system satisfies a set of conditions. This includes many relevant applications such as ground state preparation for local theories in physics or chemistry, combinatorial optimisation problems, or quantum machine learning. In particular, we analyse the quantum imaginary time evolution showing convergence guarantees to the global minimum without critical slowing down and providing a priori estimates on the required evolution time which scale linearly in system size and inverse energy gap. Furthermore, a provided complexity analysis shows that quantum imaginary time evolution can be efficiently compiled into a parametric quantum circuit, finding the optimal parameters included, for a large class of physically relevant problems.

quant-ph↗
arXiv2026

Constrained dynamics for searching saddle points on embedded Riemannian submanifolds of Euclidean space

Finding constrained saddle points on embedded Riemannian submanifolds of Euclidean space is significant for analyzing energy landscapes arising in physics and chemistry. Existing works exploit explicit global/local regular level-set representations of manifolds, which may be unavailable or computationally inconvenient for manifolds represented through, e.g., projectors, factorizations, or rank constraints. In this paper, we develop a constrained saddle dynamic based on embedded-submanifold geometric primitives, completely avoiding the use of explicit representations. In particular, our dynamic is formulated compactly on the Grassmann bundle of the tangent bundle. By analyzing the Grassmann bundle geometry, we rigorously establish the local linear stability of the dynamic and the local linear convergence of the resulting algorithms. Remarkably, our analysis provides the first iterate convergence result for discretized algorithms to saddle points of prescribed indices in embedded-submanifold settings. Moreover, by virtue of the Grassmann bundle formulation, we remove unnecessary nondegeneracy assumptions on the eigenvalues of the Riemannian Hessian that are present in existing works. We also point out that locating saddle points can be more ill-conditioned than finding local minimizers, and requires using nonredundant parametrizations. Finally, numerical experiments on linear eigenvalue problems and electronic excited-state calculations showcase the effectiveness of the proposed algorithms and corroborate the established local theory.

math.NA↗
arXiv2026

Polarizable atomic multipoles for learning long-range electrostatics

Long-range electrostatics and polarization remain central obstacles to extending machine learning interatomic potentials (MLIPs) to ionic, polar, and interfacial systems. Here we introduce a semi-local framework for learning electrostatics from energies and forces using polarizable atomic multipoles. Local equivariant descriptors predict environment-dependent latent monopoles, dipoles, and quadrupoles, while residual non-local charge transfer and polarization are captured by non-self-consistent linear response in induced charges and dipoles. Across four diverse benchmarks and four short-range MLIP architectures, the multipole hierarchy and response terms systematically improve potential energy surface accuracy, with the largest gains in systems where long-range effects are essential. More importantly, physically meaningful electrical responses emerge without direct supervision. The learned latent multipoles yield accurate Born effective charge tensors and infrared spectra in close agreement with experiments. The induced-dipole extension introduces new capabilities: it predicts polarizabilities and thereby enables semi-quantitative Raman spectra for bulk water and hybrid MAPbI$_3$ perovskite, as well as the essential features of the surface-specific vibrational sum-frequency generation spectrum at the water-air interface. In ferroelectric HfO$_2$, the predicted electrical response also captures LO-TO splitting and polarization switching. This systematically improvable, physically transparent framework enables MLIPs trained on standard energy and force labels to predict polarization-sensitive observables.

cond-mat.mtrl-sci↗
arXiv2026

Generative Diffusion Surrogates with Analytical Variance Schedule

Stochastic transport describes physical systems in which an initially structured distribution spreads under unresolved forcing, scattering, or heterogeneous media. Useful surrogates for such systems should be probabilistic, time-resolved, and able to represent non-Gaussian distributional structure. Generative diffusion models, which corrupt data with Gaussian noise and learn a reverse flow back to structured states, have these properties. Their noise schedules, however, are usually chosen heuristically: image and audio generation---the canonical use cases---provide no physical clock. In transport, by contrast, the variance, or mean-square displacement, is often known from macroscopic theory or empirical scaling even when the full distribution is not. Here we prescribe the forward noising rate as the time derivative of this variance, turning generative time into a calibrated transport clock. The variance path is enforced by construction, while the learned score field represents how non-Gaussian structure inherited from entrance data is smoothed along that path, requiring no intermediate-time physical transport data. For ballistic-to-diffusive transport in turbulent plasmas, the surrogate matches test-particle distributions, reproduces the laboratory-measured variance scale, and tracks the simulated kurtosis evolution without schedule tuning, enabling calibrated emulation and likelihood-based inference.

cs.LG↗
arXiv2026

Learning a general class of admissible multi-species collision operators from molecular dynamics

We develop a structure-preserving, data-driven collision operator for spatially homogeneous multi-species kinetic systems from molecular dynamics (MD). The operator consists of diagonal self-collision blocks and ordered off-diagonal cross-species blocks to describe intra- and inter-species momentum and energy exchange. Within a local and point-wise identifiable kernel class, we develop the necessary and sufficient condition for the admissible kernel class satisfying the conservation laws, the H-theorem, and the frame indifference. Unlike the classical Landau operator, the off-diagonal kernels are not restricted to be symmetric under permutation of the two velocity variables. This unique structural freedom captures the distinct responses of different species to unresolved correlations and many-body effects arising from micro-scale particle interactions. The equivalent parameterizable kernel formalization enables us to learn a generalized data-driven collision operator directly from MD, where the low-rank tensor representations and random sampling are used to achieve efficient kernel training and numerical simulation. Numerical experiments show that the learned operator accurately predicts transport coefficients and the non-equilibrium relaxation, while retaining discrete conservation and entropy production. In particular, it captures plasma kinetics in the moderately coupled regime, where the predictions of both the Landau and the data-driven model restricted to velocity-permutation symmetry show significant discrepancies.

physics.comp-ph↗
arXiv2026

Stochastic Optimization of Tree Tensor Networks

Tensor networks, originally developed for quantum many-body physics, are promising models for machine learning. We derive stochastic Riemannian optimizers for tree tensor networks (TTNs) on both their parameter and quotient manifolds, including adaptive and learning-rate-free schemes suitable for minibatch training. Using a hybrid CNN-TTN architecture, we evaluate the methods on Fashion-MNIST, CIFAR10, and Imagenette. The proposed optimizers achieve predictive performance comparable to unconstrained optimization while enabling numerically stable downstream compression.

math.OC↗