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47 records · Page 3Linked to original sources

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

Functional Connectivity Networks for Transportation Delay Analysis: from Theory to Software

Within the endeavour of modelling and understanding the propagation of delays in transportation networks, an approach that has attracted increasing interest in the last decade is the creation of functional network representations. These graphs map elements of interest (e.g. airports or stations) as nodes, and derive pairwise propagation patterns from their dynamics through correlation and causality tests. In spite of multiple notable results, this approach still lacks a coherent framework, with decisions related to many fundamental steps being left to the judgement of the researcher. We here provide an introduction to the theory behind functional networks for transportation systems, detailing the main steps and the associated pitfalls. We further introduce a Python package, delaynet, designed to support the researcher in the reconstruction and analysis of such networks. We finally present an analysis of the propagation of delays in the Swiss train system; and discuss future research steps.

physics.soc-ph↗

arXiv2026

NORi: An ML-Augmented Ocean Boundary Layer Parameterization

NORi is a machine learning (ML) parameterization of ocean boundary layer turbulence that is physics-based and augmented with neural networks. NORi stands for neural ordinary differential equations (NODEs) Richardson number (Ri) closure. The physical parameterization is controlled by a Richardson number-dependent diffusivity and viscosity. The neural ODEs are trained to capture the entrainment through the base of the boundary layer, which cannot be represented with a local diffusive closure. The parameterization is trained using large-eddy simulations in an a posteriori fashion, where parameters are calibrated with a loss function that explicitly depends on the actual time-integrated variables of interest rather than the instantaneous subgrid fluxes, which are inherently noisy. NORi conserves tracers by design, uses realistic nonlinear thermodynamics, and demonstrates excellent prediction and generalization capabilities in capturing entrainment dynamics under different convective strengths, background stratifications, rotation, and wind forcings. NORi is shown to simulate the seasonal evolution of the boundary layer at Ocean Weather Station Papa with similar performance to the state-of-the-art two-equation k-epsilon closure. When implemented in a double-gyre simulation, it is numerically stable for at least 100 years, despite only being trained on two-day horizons, and can be run with time steps as long as one hour. Combining highly expressive neural networks with a physically grounded base closure proves to be a robust paradigm for designing parameterizations for climate models: data required and training cost are drastically reduced, inference performance can be directly optimized as a primary objective, and numerical stability is implicitly promoted through training.

physics.ao-ph↗

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

Higher order stray field computation on tensor product domains

We present an extension of the tensor grid method for stray field computation on rectangular domains that incorporates higher-order basis functions. Both the magnetization and the resulting magnetic field are represented using higher-order B-spline bases, which allow for increased accuracy and smoothness. The method employs a super-potential formulation, which circumvents the need to convolve with a singular kernel. The field is represented with high accuracy as a functional Tucker tensor, leveraging separable expansions on the tensor product domain and trained via a multilinear extension of the extreme learning machine methodology. Unlike conventional grid-based methods, the proposed mesh-free approach allows for continuous field evaluation. Numerical experiments confirm the accuracy and efficiency of the proposed method, demonstrating exponential convergence of the energy and linear computational scaling with respect to the multilinear expansion rank.

physics.comp-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↗