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physics.comp-ph

physics.comp-ph: explore 31 source-linked works published from 2025 to 2026, with original documents and citations.

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Includes records with this source-supplied label or an explicit phrase match in their metadata. Matches indicate a mention, not proof that a paper uses a method or tests a material. Source versions are consolidated by DOI.

Sources: arxiv. Collection updated 2026-09-15. Counts describe this index, not the complete source archives.

arXiv2026

A Spectral Identifiability Threshold for Dissipative Rate Recovery from Truncated Liouvillian Spectra

Open quantum systems lose energy and phase coherence through different dissipative processes, but these processes can produce overlapping dynamical signatures. The Liouvillian spectrum summarizes how such a system relaxes, yet it is not obvious how much of that spectrum is needed to distinguish the underlying dissipation rates. We study this question for amplitude damping and dephasing in a six-qubit Lindblad model whose spectrum can be derived analytically. We retain only the slowest non-steady spectral modes and ask how many are required before each dissipative rate becomes recoverable. We show that population modes contain no dephasing information, which creates a lower bound of D = 2^n retained modes for uniform dephasing identifiability in the relevant rate regime. The measured recovery threshold reaches this bound at n = 4,5,6, while n = 3 remains above it. At n = 6, least squares achieves a mean joint absolute error of order 10^-9, compared with 4.355 x 10^-4 for four tabular learning methods. Robustness tests show that this advantage weakens when the spectra are perturbed and when a transverse field breaks the commuting structure. These results show that the amount and structure of retained spectral information can determine whether dissipative parameters are recoverable, independently of the estimator used. The present conclusions apply to noise-free simulator spectra rather than measurement-derived spectra.

cs.LG↗

arXiv2026

Examining the robustness of Physics-Informed Neural Networks to noise for Inverse Problems

Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for which many properties and limitations remain unknown. PINNs are widely accepted as less computationally efficient and accurate than traditional methods for solving PDEs, such as the finite element method. However, PINNs are commonly claimed to show promise in solving inverse problems and handling noisy or incomplete data. We compare the performance of PINNs in solving inverse problems with that of a traditional approach using the finite element method combined with a numerical optimizer. The models are tested on viscosity identification in 1D Burgers' equation and in 2D/3D Taylor-Green Vortex, in all cases with additive Gaussian noise applied to training and validation data. We find that while PINNs may require less human effort and specialized knowledge, they are outperformed by the traditional approach. For example, for 2D Taylor-Green Vortex with $σ$=1 noise, the baseline has a mean prediction RMSE of 0.0013 compared to 0.01 for the best PINN variation. However, PINNs scale better than the baseline with the computational complexity of the problem. We identify failures during training to be addressed if the PINN performance on noisy inverse problems is to become more competitive.

physics.comp-ph↗

arXiv2026

Operator Learning for Predicting Bulk Wave Parameters of Spectral Wave Models

The impact of wave-induced forcing on the mean water level and nearshore currents is typically modeled through excess momentum fluxes, also known as radiation stresses, and their spatial gradients. Accurate storm surge prediction requires coupled circulation and wave models, but the high computational cost of numerical wave models limits their temporal resolution. In this work, we explore a proof-of-concept application of Deep Operator Networks (DeepONets) as a surrogate for the Simulating WAves Nearshore (SWAN) numerical wave model. Unlike grid-dependent surrogate models, DeepONets learn the underlying continuous operator, and thus, can provide highly efficient prediction while enabling discretization-invariant inference. The proposed surrogate model is evaluated using two distinct 1-D and 2-D steady-state numerical examples with variable boundary wave conditions and wind fields. When applied to a realistic numerical example of steady-state wave simulation in Duck, NC, the DeepONet surrogate improves computational efficiency by four orders of magnitude. Furthermore, the model demonstrates consistently high accuracy in predicting the significant wave height and the x- and y- components of the radiation stress gradient, by achieving relative L_2 errors bounded by 1.91%, 10.98%, and 6.88%, respectively, across all unseen test scenarios.

physics.comp-ph↗

arXiv2026

SDF-Aware Weighting: Adaptive Eikonal Regularisation for Three-Dimensional Level-Set Physics-Informed Neural Networks

Adaptive loss-balancing schemes for physics-informed neural networks rest on a premise that every residual should be driven to zero. For level-set advection with an eikonal regulariser that premise fails: the eikonal term penalises deviation of $\lVert\nablaϕ\rVert$ from unity, a property transport preserves only under rigid motion; where the exact solution departs from a signed-distance function the eikonal residual of the correct answer is nonzero, and driving it to zero moves the network away from that answer. We show that standard gradient-norm balancing fails in exactly this way, its weight remaining near its initial value throughout training on benchmarks where the property is violated, and we introduce SDF-Aware Weighting (SAW), which combines a residual-quantile gate with a gradient-norm ratio so that points exhibiting legitimate departure are excluded before the surviving term is scaled. Across four three-dimensional benchmarks SAW selects an eikonal weight within an order of magnitude of the value located by an eighteen-run manual sweep, spanning four decades from $10^{-1}$ to $10^{-5}$ with a single fixed configuration. On the slotted sphere, where the initial field is non-differentiable at reentrant edges, SAW attains a lower error than any weight in that sweep. Two smooth rigid benchmarks serve as controls: SAW is worse there, as expected when its premise does not hold. An ablation with the gate disabled shows the slot is nearly entirely filled while the relative $L_2$ error reads $1.06\%$, indistinguishable from a field that never represented the slot. We give a feature-restricted measure that separates the two cases.

physics.flu-dyn↗

arXiv2026

Beyond Pairwise Graphs in Science: Hypergraph Adaptive Wavelet Operators for Parametric PDEs

Physical systems are often modeled by solution operators that map input fields, parameters, geometries, or past states to steady or future physical states. Learning these maps is difficult, especially for time-dependent systems that must assimilate history and remain stable under autoregressive rollout. Many neural operators work best on regular, structured grids, while realistic simulations often require unstructured meshes or point clouds to resolve complex geometries; in such settings, grid-centric representations can lose accuracy. Graph neural operators handle these domains through message passing or spectral graph filtering, but pairwise edges do not directly capture group-wise couplings among mesh cells, local neighborhoods, or conservation volumes. We introduce the Hypergraph Adaptive waveLet Operator (HALO), which lifts the domain to a hypergraph and learns in its spectral wavelet domain. HALO avoids explicit hypergraph-Laplacian eigendecomposition through Chebyshev polynomial wavelet filters, giving localized spectral kernels at linear sparse-matrix cost. Its trainable dyadic wavelet scales are regularized toward tight-frame coverage, allowing the frequency response to adapt to each PDE while encouraging stable multi-scale spectral coverage. Across 2D and 3D benchmarks on structured and unstructured discretizations, HALO achieves best or near-best accuracy among frequency-, transformer-, DeepONet-, state-space-, and graph-based baselines and sustains stable multi-step rollouts. The same model scales to industrial aerodynamic geometries: on meshes of a few hundred thousand points it is on par with, or better than, the strongest fixed-discretization transformers, while remaining resolution-equivariant.

cs.LG↗

arXiv2026

Accelerated S-NFC for Million-Chaff RCS Computation Using Low-Rank Compression of Concatenated Block Rows

Sparsification via neglecting far-field coupling (S-NFC) enables fast full-wave radar-cross-section analysis of large-scale chaff clouds by retaining only significant local electromagnetic interactions. This letter further accelerates S-NFC by concatenating the retained off-diagonal interaction blocks associated with each receiving chaff element and applying a joint low-rank factorization with a shared receiving-side basis. Exact self interactions are preserved, while repeated chaff templates reuse precomputed lower--upper factorizations of the self-interaction blocks. The compressed formulation reduces retained-coupling storage and matrix--vector multiplication cost and also decreases the number of iterations required by the generalized conjugate residual solver. Numerical tests with 100,000 chaff elements demonstrate sub-$1\%$ complex-far-field error for low-rank approximations in sparse regimes and identify a practical self-only limit at sufficiently large mean spacing. For a one-million-chaff plume, the proposed compressed S-NFC achieves a $6.92\times$ end-to-end speedup over uncompressed S-NFC while storing only $6.60\%$ of the retained coupling, with a complex-far-field error of $0.253\%$.

physics.comp-ph↗

arXiv2026

Real-Time Monitoring of MHD Liquid Metal Flows with Shallow Recurrent Decoders

State estimation in magnetohydrodynamic flows is critical for real-time monitoring of liquid metal blankets in tokamak fusion reactors. Due to the multiphysics nature of these phenomena, high-fidelity simulations are computationally prohibitive for real-time applications. This work investigates a data- driven Reduced Order Model framework: the Shallow Recurrent Decoder (SHRED) coupled with Principal Component Analysis, to map sparse temperature measurements to the full thermo-hydraulic system's state. The major contribution of this work lies in the two-parameter analysis of a fully three-dimensional domain representative of the DEMO breeding blanket configuration. Here, the flow is subjected to an external magnetic field varying in direction and intensity and is hindered by two cylinders acting as a water-cooling system, which impose a temperature boundary condition on their surfaces. This double-parametric magnetic variation induces nonlinear transitions in the flow dynamics, ranging from chaotic behavior at low magnetic field intensities to laminarized regimes at high intensities, characterized by the formation of asymmetric side layers at an inclination angle of 30 degrees. SHRED reconstruction maintains a mean relative error of approximately 5% for the temperature, pressure, and velocity fields. This accuracy is maintained across both weak and strong magnetic fields, ranging from 0.075 T to 0.300 T, and for inclination angles from 5 to 30 degrees, reflecting its dominant toroidal component. These errors are only slightly larger than the lower error bound dictated by low-rank truncation. The results establish SHRED as a reliable state estimator for complex and realistic engineering applications involving completely unseen parametric scenarios and validate it as an accurate real-time state estimation technique suitable for online monitoring and control of real facilities.

physics.comp-ph↗

arXiv2026

High-Order-Accurate Continuity Enforcing Nyström Discretization of 3D Maxwell Combined Field Integral Equations

In Nyström-collocation discretizations of the electric field integral equation (EFIE), the surface divergence acts on surface densities that may be discontinuous across patch boundaries, which degrades accuracy and convergence. We show that this not only affects the EFIE but every formulation in which the operator occurs, either in the equation itself or in the scattered field computation, and propose a high-order-accurate continuity-enforcing scheme for smooth surfaces as a remedy for the direct and indirect EFIEs, magnetic field integral equations (MFIEs), and regularized combined field integral equations (CFIEs) alike. The scheme comprises two ingredients: i) We show how to discretize the equations via a Chebyshev-based Nyström scheme, which admits closed quadrature rules. ii) Since unknowns and test vectors are in terms of patch-local curvilinear bases, continuity is enforced by a change of basis: we construct sparse mapping matrices assembled solely from the curvilinear geometry description. In doing so, we restore the accuracy of the EFIE such that it can be combined with the MFIEs with equal weights to form CFIEs. Numerical studies for the scattering from canonical and realistic geometries show that all considered formulations individually and combined benefit from the continuity enforcement in terms of better conditioning, reduced iterations of an iterative solver, and several more digits of accuracy in the scattered fields, despite reducing the total number of unknowns.

math.NA↗

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

Propensity Straight-Through Gradients for Discrete Stochastic Systems

Continuous-time Markov chains (CTMCs) provide the backbone for modeling discrete stochastic dynamics across applied, physical, and biological sciences. Their integration with modern gradient-based machine learning, however, is limited by the hard categorical event selection intrinsic to Gillespie-type simulation algorithms. We exploit the affine state update to obtain the exact one-step conditional-mean sensitivity by differentiating normalized reaction propensities. We pair this backward rule with exact forward trajectories to define the propensity straight-through (PST) estimator. At the trajectory level, we show that one-step sensitivities composed across events can depart from the exact multistep sensitivity. We derive the resulting per-step discrepancy in closed form and prove that it vanishes identically for affine downstream dependence. PST matches the accuracy of Gumbel-Softmax straight-through across all benchmarks: reversible dimerization (0.06% error), a genetic oscillator (1.7% error), a 50-task repressilator suite (0.17% median error), and patch-clamp ion-channel recordings ($R^2$ = 0.988). Under matched settings, PST converges 3.0-fold faster on the oscillator and 2.1-fold faster on the ion channel. At deep-learning scale, PST trains a 203,796-parameter stochastic reaction network with hard sampling, reaching 98.22% MNIST digit classification accuracy. By differentiating an exact conditional mean rather than a relaxed sample, PST offers a temperature- and Gumbel-free path to scalable gradient-based learning through exact stochastic trajectories.

q-bio.QM↗

arXiv2026

A Framework Integrating the Dynamic Stiffness Matrix with Physics-Informed Neural Networks for Solving Eigenvalue Problems and Analysing Dynamic Response

This paper introduces a framework that integrates the dynamic stiffness matrix (DSM) with physics-informed neural networks (PINN). The DSM-PINN embeds physical constraints within the model and demonstrates robustness, particularly when addressing limited datasets across diverse investigations. In this approach, deep neural network outputs approximate the displacement fields of element nodes. Unlike the finite element method (FEM), the element shape functions are homogeneous solutions to the governing partial differential equation, forming the basis of the exact dynamic stiffness matrix, thereby avoiding high-order derivative terms. This matrix also serves as a frequency-domain spectral element, resulting in a strong-form PINN. The loss function is produced by connecting neural networks with dynamic stiffness matrices. We focus on utilising PINNs to resolve eigenvalue problems by employing the Wittrick-Williams algorithm, which overcomes the challenge of neural networks failing to converge to higher-order eigenvalues. Additionally, the frequency domain-PINN method is used to analyse structural dynamic responses under moving and impulsive loads, addressing the limitation of neural networks in handling complex numbers. Theoretical convergence stability of the suggested approach is also analysed even DSM is an indefinite matrix after implementing the boundary condition. The numerical results validate the practicality and efficacy of the recommended approach.

math.NA↗

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↗

arXiv2025

Reinforcement learning framework for the mechanical design of microelectronic components under multiphysics constraints

This study focuses on the development of reinforcement learning based techniques for the design of microelectronic components under multiphysics constraints. While traditional design approaches based on global optimization approaches are effective when dealing with a small number of design parameters, as the complexity of the solution space and of the constraints increases different techniques are needed. This is an important reason that makes the design and optimization of microelectronic components (characterized by large solution space and multiphysics constraints) very challenging for traditional methods. By taking as prototypical elements an application-specific integrated circuit (ASIC) and a heterogeneously integrated (HI) interposer, we develop and numerically test an optimization framework based on reinforcement learning (RL). More specifically, we consider the optimization of the bonded interconnect geometry for an ASIC chip as well as the placement of components on a HI interposer while satisfying thermoelastic and design constraints. This placement problem is particularly interesting because it features a high-dimensional solution space.

physics.comp-ph↗

Compare source metadata on this page

Work	Published	Source identifier	Source
A Spectral Identifiability Threshold for Dissipative Rate Recovery from Truncated Liouvillian Spectra	2026-08-29	2608.29302	arxiv
Examining the robustness of Physics-Informed Neural Networks to noise for Inverse Problems	2026-08-28	2509.20191	arxiv
Operator Learning for Predicting Bulk Wave Parameters of Spectral Wave Models	2026-08-28	2604.06433	arxiv
SDF-Aware Weighting: Adaptive Eikonal Regularisation for Three-Dimensional Level-Set Physics-Informed Neural Networks	2026-08-28	2608.08322	arxiv
Beyond Pairwise Graphs in Science: Hypergraph Adaptive Wavelet Operators for Parametric PDEs	2026-08-28	2608.27883	arxiv
Accelerated S-NFC for Million-Chaff RCS Computation Using Low-Rank Compression of Concatenated Block Rows	2026-08-28	2608.27936	arxiv
Real-Time Monitoring of MHD Liquid Metal Flows with Shallow Recurrent Decoders	2026-08-28	2608.28366	arxiv
High-Order-Accurate Continuity Enforcing Nyström Discretization of 3D Maxwell Combined Field Integral Equations	2026-08-28	2608.28876	arxiv
Physics-informed learning for the inverse problem in resonant ultrasound spectroscopy	2026-08-27	2608.27590	arxiv
Propensity Straight-Through Gradients for Discrete Stochastic Systems	2026-08-26	2608.25631	arxiv
A Framework Integrating the Dynamic Stiffness Matrix with Physics-Informed Neural Networks for Solving Eigenvalue Problems and Analysing Dynamic Response	2026-08-26	2608.28683	arxiv
Geometric integrators for adiabatically closed simple thermodynamic systems	2026-02-01	2511.14154	arxiv
Reinforcement learning framework for the mechanical design of microelectronic components under multiphysics constraints	2025-04-23	2504.17142	arxiv

These are bibliographic comparisons, not experimental rankings. Follow the original document for methods and conditions.