Papers
Machine learning for physics, as it is published.
New work from arXiv on CFD surrogates, neural operators and physics-informed learning, refreshed every hour. Search it, filter by topic, or start with the papers we keep coming back to.
Papers
New work from arXiv on CFD surrogates, neural operators and physics-informed learning, refreshed every hour. Search it, filter by topic, or start with the papers we keep coming back to.
4,567 papers in Physics-informed · newest first
math.AP
In this work we address a class of Mean-Field Game (MFG) systems on the flat torus in which individual agent incentives arise from macroscopic, distribution-dependent objectives governed by the Wasserstein-2 () distance. Taking the first variation (Lions derivative) of the Wasserstein-based macroscopic functional yields a coupled forward-backward system of Hamilton–Jacobi–Bellman (HJB) and Fokker–Planck (FP) equations featuring a nonlocal coupling driven by the Kantorovich optimal transport potential. As a primary case study, we formulate a large-scale attacker-defender attrition model aimed at protecting High-Value Units (HVUs). By defining population-wise attrition rates via the metric and casting the defense strategy as a Pareto-optimal McKean–Vlasov control problem, we derive a concrete HJB–FP system with a Kantorovich potential coupling. We prove the local-in-time existence of classical solutions for this system using Schauder's fixed-point theorem. Finally, we compute the MFG dynamics by combining the Sinkhorn algorithm with ResNet-based Physics-Informed Neural Networks (PINNs), and simulate two-dimensional attacker-defender engagements across diverse attrition parameters, control costs, and multi-HVU configurations.
cs.LG
Machine learning for powder diffraction (PXRD) symmetry classification is being trained at scale, yet the field lacks a common evaluation standard: papers report results on different subsets of experimental archives, with different target taxonomies, preprocessing, and metrics, and published models are rarely released in a form that permits rescoring. We present InformedXRD, an evaluation framework with three parts: (i) a machine-readable mapping from 230 space groups to 99 extinction groups, the finest classes powder diffraction can identify from systematic absences alone; (ii) a benchmark-construction method whose inclusion rules are specified as code and reproduce from a frozen snapshot, instantiated as RRUFF-473, RRUFF-325, and, as a small example, opXRD-98; (iii) a reporting protocol with prior-only frequency baselines, a label-permutation test, a hierarchy-aware error metric on the condensed translationengleiche subgroup graph, and stratified evaluation. We build on the mapping, RRUFF benchmarks, subgroup graph, and four ViT checkpoints released in our earlier work (Baggett et al., 2026). Using these checkpoints, a 1D residual CNN, and six architectures trained under the XRDBench recipe (Cao et al., 2025), we show that evaluation design changes what conclusions are justified: paired tests point in different directions at Top-1 and Top-5; paired Top-k tests do not separate the three leading XRDBench models, while hierarchy-aware analysis describes error distance and direction across all six; an input-blind frequency predictor matches the models on aggregate Top-k, yet a label-permutation test still detects pattern-specific evidence; and stratified analysis exposes a label-entropy confound that aggregate accuracy hides. All mapping tables, benchmark code, scripts, and checkpoints are released as shared infrastructure for PXRD-ML evaluation.
physics.space-ph
The solar-wind speed at the inner boundary of heliospheric models is not observed; near-Earth monitors record the wind only after nonlinear propagation. We pose the reconstruction of an effective boundary speed at as an inverse problem and train a map from solar observations to that boundary by differentiating through a reduced heliospheric transport solver from 21.5 to measurement locations near the L1 Lagrangian point. Screening 42 candidate features from SDO/AIA 193~Å images and SDO/HMI magnetograms identifies coronal-hole area, its proximity to the ecliptic and its darkness as the most informative; the reference model adds their recent history, the expansion factor of GONG-based potential-field models and the speed observed one rotation earlier. In five-fold chronological cross-validation over solar cycle 24, the reconstruction outperforms 27-day recurrence and a linear regression on the screened features at a fixed lead (ROC area for wind above 600~km~s: 0.879 versus 0.802 and 0.850) with a predicted-to-observed standard-deviation ratio of 0.81, at the cost of a ~km~s bias from its tail-weighted loss. A factorial comparison shows that the skill comes from training through a speed-dependent propagation: a fixed lag degrades the score by 8.6~km~s, stream interaction adds little, and a linear map, or a model with one coefficient per physical quantity, matches the neural network. About 57% of the variance of the hourly speed is not determined by these inputs, and the remaining error is common to all model classes: better reconstructions need more informative inputs rather than more flexible models. Forecasting and probabilistic prediction are addressed in Parts II and III.
cs.CV
Reconstructing physical dynamics from fixed sparse sensors and missing frames is a fundamental challenge in scientific research. Sparsity leaves large regions of the field unconstrained, making the inverse problem ill-posed: a model may fit the observed sensors while producing inaccurate off-sensor structures or unreliable predictions between support frames. To this end, we propose PhysFTM—a physics-informed functional Tucker model that parameterizes the Tucker mode factors in reproducing kernel Hilbert spaces (RKHSs) and incorporates PDE constraints through finite-difference residuals evaluated at off-sensor collocation points. These residuals provide additional physical information in regions without direct observational supervision. PhysFTM first reconstructs continuous spatial fields at support frames via an alternating minimization scheme, optimizing the Tucker core tensor and the RKHS-based factors separately. To enable missing-frame reconstruction, PhysFTM constructs a continuous trajectory in Tucker-core space, which is decoded by the learned spatial RKHS-FTM representation to recover the full spatiotemporal field. Experiments on Allen–Cahn, Navier–Stokes, three-dimensional Heat equations, and a three-dimensional gridded Copernicus ocean reanalysis demonstrate accurate 2D/3D reconstruction under two missing-frame protocols. Code is available at https://github.com/liusirzzz/PhysFTM.
math-ph
The Lane-Emden Equation is a class of nonlinear differential equations commonly used to model phenomena in astrophysics and mathematical physics, such as stellar structure and thermal behavior in polytropic gas spheres. This study presents a novel hybrid framework that integrates Physics-Informed Neural Networks (PINNs) with boosting methods to enhance the accuracy and robustness of solutions for Lane-Emden type differential equations. Standard PINNs leverage physical laws encoded within the loss function, but their predictive performance can be constrained by optimization challenges and approximation errors. To address this, we introduce a post-processing boosting stage where the residual errors from the PINN prediction are modeled using some regression algorithms - including LightGBM, Random Forest, XGBoost, and Support Vector Regression (SVR). The outputs from these boosted models are aggregated to generate a corrected, high-fidelity prediction. The proposed methodology is systematically validated through quantitative metrics and comparative analysis against the standard PINN baseline. The results demonstrate that the boosted PINN framework significantly reduces prediction error, and improves generalization, offering a powerful and flexible approach for solving scientific and engineering problems governed by differential equations.
cond-mat.mes-hall
Three-dimensional spin textures are stabilized by microscopic interactions within their host materials. X-ray vector tomography can image these nanoscale structures, but weak magnetic contrast and a limited range of viewing angles often leave parts of the magnetization poorly determined. Here we show that a reconstruction constrained by the micromagnetic energy recovers the three-dimensional magnetization from such data and gains sensitivity to the underlying material interactions. Applied to the chiral magnet CoZnMn, the method resolves the three-dimensional helical texture even from a small fraction of the dual-axis projections typically required for a successful tomographic reconstruction, or from a single tilt axis alone. By testing which ratio of exchange to Dzyaloshinskii-Moriya interaction in the reconstruction best reproduces the measured projections, we obtain a value for the sample that differs by about 10 % from the literature value derived from the helical winding period. Taken together, our findings suggest a way to reduce the time needed for vector tomography and to extend it to determining fundamental magnetic interactions in a material.
physics.app-ph
Microreactors require nonintrusive monitoring methods that can provide information about internal control states without opening or modifying the sealed system. In heat pipe microreactors, rotating control drums regulate reactivity by changing the angular orientation of neutron absorber coatings around the reflector region. This study applies the previously developed TRec muon scattering tomography framework to absorber coating localization in the heat pipe microreactor geometry. Momentum informed -value imaging is used with the spectrometer information to evaluate whether the angular orientation of absorber coatings on twelve control drums can be inferred from reconstructed muon scattering images. Two absorber materials are considered. Hafnium is used as a high contrast reference case, while boron carbide, , is used as the primary low contrast case because its density is close to that of the surrounding beryllium reflector. Both laser generated and cosmic ray muon sources are evaluated for absorber-in and absorber-out drum configurations. The reconstructed transverse images and one dimensional drum profiles show clear hafnium localization with both source types. For , absorber localization is achieved with the controlled laser generated source when the number of events is increased, while the cosmic ray case remains limited by weak absorber contrast and artifacts near high scattering regions. The study defines the imaging conditions under which TRec based -value tomography can support control drum absorber localization for passive microreactor monitoring. These findings also support safeguards by design by informing the selection of absorber and reflector materials, dimensions, and coating thickness that improve nonintrusive detectability.
physics.flu-dyn
Physics informed machine learning provides a framework to study and simulate fluid dynamics, potentially at a fraction of the computational cost of traditional numerical methods, with the goal of improving the explainability, accuracy and robustness of purely data driven machine learning methods. In this work, we extend the hard constraint projection (HCP) method developed by Chen et al. [Journal of Computational Physics, 445, 110624, 2021] from a linear partial differential equation (PDE) to a nonlinear PDE: the 1D Burgers' equation. To strictly impose a discrete approximation of the governing equation, the Burgers' equation is first locally discretised (using a finite difference stencil) then decomposed into a constraint matrix and a prediction matrix. Using tools from linear algebra, the constraint matrix is used to construct a projection matrix. A physics informed neural network (PINN) [Raissi et al. Journal of Computational Physics, 378, 686, 2019] is used to predict the velocity, and a final unlearnable layer projects the velocity prediction to the hyperplane of exact solutions to a discretised form of the Burgers' equation. Our initial results indicate that the HCP-PINN initially trains similarly to an equivalent PINN, and as the PINN loss plateaus, the HCP-PINN loss continues to decline. When tested on a previously unseen uniform grid of points covering the domain, the HCP-PINN exhibits higher accuracy, converging to a data error approximately an order of magnitude lower than the comparable PINN. We also observe that the inclusion of the HCP layer results in better observance of the governing PDE. Our findings suggest that the HCP-PINN can be more robust to the selection of physics collocation points, and less dependent on collocation point quantity.
physics.flu-dyn
Detailed chemical kinetic mechanisms are computationally expensive in reacting-flow simulations because of their high dimensionality and numerical stiffness. We develop an end-to-end physics-informed autoencoder neural ordinary differential equation (PI-AE-NODE) framework in which an encoder compresses the thermochemical state into a low-dimensional latent space, a Neural ODE advances it continuously in time, and a decoder reconstructs the temperature and all species mass fractions. Elemental conservation, mass conservation, and enthalpy consistency are embedded in the training objective. The framework is applied to H/air, NH/air, and CH/air autoignition using detailed mechanisms of increasing size and complexity, which are represented accurately with only a few latent variables. Compared with an otherwise identical data-driven model, the physical constraints improve ignition delay prediction and conservation behaviour. The models reproduce major and intermediate species evolution at both training and unseen conditions, and their latent dynamics permit efficient explicit integration, with the computational advantage over the detailed mechanisms increasing with mechanism size.
hep-lat
We construct a generative network for Monte-Carlo sampling in lattice field theories and beyond, for which the layerwise propagation is computed and optimised independently on each layer. The architecture uses physics-informed renormalisation group flows that provide access to the layerwise propagation step from one layer to the next in terms of a simple first order partial differential equation for the respective renormalisation group kernel through a given layer. Thus, it transforms the generative task into that of solving once the set of independent and linear differential equations for the kernels of the transformation. As these equations are analytically known, the kernels can be refined iteratively. This allows us to structurally tackle out-of-domain problems generally encountered in generative models and opens the path to further optimisation. We illustrate the practical feasibility of the architecture within simulations in scalar field theories.
cs.CE
Physics Informed Neural Networks offer a mesh-free approach to solving differential equations, but their application to time-dependent problems remains challenging, particularly when the governing dynamics involve widely different time scales. With collocation points spread uniformly in time, short intervals of rapid change are under resolved. This work introduces an equation informed time reparameterization framework that modifies the temporal coordinate used during PINN training based on the local dynamics of the governing equation. The proposed method follows a two stage procedure. First, a pilot PINN training provides an approximate solution, which is used to linearize the governing differential operator and estimate its local response to small perturbations. These responses are combined into a time-dependent rate function, large where the dynamics are fast, that defines a strictly increasing transformation from physical time to a new computational time coordinate. A second PINN is then trained on the transformed governing equation, with uniformly sampled collocation points in the new coordinate producing a nonuniform distribution in physical time. Different combination rules and spatial reduction strategies are considered. With the cost of the pilot training included, the method reduces the error by a factor of 4 to 29 relative to the best alternative method on the Kachanov Rabotnov creep-damage model near rupture, and by a factor of 5 to 16 relative to every alternative method on the Frank-Kamenetskii equation near blow up.
cs.LG
We develop an uncertainty-aware physics-informed surrogate for a one-dimensional - junction diode, conditioned on device length, doping and bias. Using the internal state of the device as predicted by the surrogate we develop a test-suite of quantities of interest including the terminal current, depletion width, peak field and stored charge. The formalism and the quantities are can be extended to asymmetric junction and two-dimensional diodes as shown by means of benchmark analysis. For the one-dimensional symmetric junction surrogate, we obtain 0.11% median error on the electrostatic potential, and 1.5% and 0.61% on the electron and hole densities. Finally, we develop an uncertainty analysis which determines the validity of surrogate answer within the user-specified tolerance.
cs.LG
Physics-informed machine learning (PIML) and hybrid modeling have attracted significant attention as approaches for combining physical knowledge with the flexibility of deep learning. In this work, we investigate whether these approaches deliver their commonly claimed benefits for large-scale photovoltaic (PV) power forecasting. We develop two hybrid forecasting architectures that integrate the ADR physical PV efficiency model with the TSMixer neural forecasting architecture through feature augmentation and residual learning. The proposed models are evaluated on a dataset comprising over 3 million samples from 3,713 PV installations across 33 European countries. We assess convergence speed, forecasting accuracy, transferability across geographical regions, and data efficiency. Although the physics-informed models seem to exhibit slightly faster convergence during training, they do not achieve consistent improvements in test-set accuracy, generalization, or performance under limited training data compared to the purely data-driven baseline. These findings suggest that, for modern deep forecasting architectures trained on large datasets, explicitly incorporating the ADR physical model provides limited practical benefit for day-ahead PV forecasting.
physics.flu-dyn
We investigate the influence of non-dimensionalization on the trainability and accuracy of physics-informed neural networks (PINNs) for buoyancy-driven flows. Using a differentially heated square cavity at and –, we compare thermal-diffusive and free-fall velocity scalings under identical training conditions. The free-fall scaling, with a unit buoyancy coefficient, achieves errors below 1.1% in the mean Nusselt number for , whereas the diffusive scaling, with a buoyancy coefficient of , produces errors of 157–650% and diverges at . We identify a coefficient-induced gradient imbalance, with the dominant buoyancy-related contribution to the loss gradient scaling as , and confirm it through direct gradient measurements. Neither sparse-data supervision nor adaptive loss weighting resolves the training difficulties under the tested conditions. For unsteady convection, the free-fall PINN accurately predicts long-time heat transfer but fails to capture the transient Nusselt-number overshoot. These findings establish non-dimensionalization as an important design consideration for improving PINN trainability in buoyancy-driven flows.
physics.flu-dyn
Deep lid-driven cavities contain strong motion beneath the lid and much weaker recirculation at depth, so agreement in bulk velocity is an incomplete assessment of a computed flow. We examine data-free physics-informed neural networks (PINNs) for steady, two-dimensional incompressible flow in a cavity of depth-to-width ratio five at Reynolds numbers 100, 250, 500 and 1000. An established hard-constrained streamfunction formulation is combined with prescribed regional collocation, transferred initialization, and selected residual-scaling and envelope variants. Independent spectral/ calculations with the same Gaussian-regularized lid provide the reference fields. For a cavity of depth-to-width ratio at Reynolds numbers , 250, 500, and 1000, evaluation on a common grid gives interior relative velocity discrepancies of 5.130%–7.850%. Over the same cases, floor-region relative velocity discrepancies remain below 5%, with absolute RMS discrepancies ranging from to , where is the lid-velocity scale. In a separate assessment at $\Rey=1000$, the refined workflow lowers interior velocity discrepancy from 5.624% to 2.658% and gauge-aligned pressure RMS discrepancy from to . The improvements compare accumulated training workflows and do not isolate regional sampling. Configuration rankings depend on both region and observable. These finite-budget comparisons establish where the retained workflows agree with the reference and where rotational-field discrepancies remain substantial.
eess.SP
Reverberation artifact suppression in ultrafast plane-wave (PW) imaging remains challenging because artifact-free reference data are generally unavailable and multipath echoes often resemble tissue signals. Coherent plane-wave compounding (CPWC) attenuates reverberation only partially and sacrifices the frame rate that motivates PW imaging. We propose pCoRev, an unsupervised physics-informed contrastive learning framework that leverages the distinct angular coherence characteristics of tissue echoes and reverberation artifacts. A single-angle I/Q frame is the network input, and the remaining angles of the same CPWC acquisition provide angle-consistent positive pairs, residual-derived negative pairs, and coherence-guided self-supervision, so no paired artifact-free data are required. On a fabricated reverberation phantom with 31 validation acquisitions, pCoRev achieved the best contrast ratio (CR), contrast-to-noise ratio (CNR), and generalized CNR (gCNR) of 38.76 +/- 5.40 dB, 11.75 +/- 1.81 dB, and 0.932 +/- 0.051 against delay-and-sum (DAS), delay-multiply-and-sum, a supervised 3D convolutional neural network, and unsupervised deep coherence learning. Because the network is trained on single-angle inputs, it also operates on a single PW transmission: with one angle, pCoRev reached a CR of 32.10 +/- 7.79 dB and a CNR of 10.39 +/- 3.02 dB, exceeding 75-angle compounded DAS (20.45 +/- 3.84 dB and 8.38 +/- 2.00 dB) with 75-fold fewer transmissions. On four clinical acquisitions from other scanners, pCoRev improved CR over DAS by 9 to 21 dB without fine-tuning. These results indicate that physics-informed unsupervised contrastive learning suppresses reverberation effectively while preserving the frame-rate advantage of ultrafast PW imaging.
cs.LG
Physics-informed holomorphic neural networks (PIHNNs) exploit complex-analytic representations to satisfy homogeneous PDEs by construction, but their extension to nonhomogeneous problems is nontrivial. We propose a hybrid physics-informed holomorphic neural network (HPIHNN) framework based on a decomposition of the solution into particular and homogeneous components. The particular component is computed by a spectral method on a simple extended domain, while the homogeneous component is approximated by a PIHNN trained only on the boundary with modified boundary data. The resulting formulation avoids meshing complex geometries and retains the dimensionality-reduction advantage of holomorphic representations. The method is applied to nonhomogeneous Poisson, Stokes, biharmonic, linear elasticity, and Helmholtz equations. Numerical experiments covering complex geometries, corner singularities, and nearly incompressible regimes demonstrate that the proposed method accurately resolves the corresponding solutions and, in the considered tests, generally achieves lower errors and shorter training times than standard PINNs. The results indicate that coupling spectral particular solutions with holomorphic neural approximations provides an efficient approach to nonhomogeneous PDEs on complex domains.
math.DG
Visualizing geodesic structures associated with general Riemannian metrics is a challenging problem in computational differential geometry. In this work, we present a computational framework for visualizing geodesics and geodesic spheres on a three-dimensional Riemannian manifold equipped with the metric . The associated Christoffel symbols and curvature tensors are computed symbolically, and the resulting geodesic equations are solved using both \texttt{SciPy}'s numerical integration method and a Physics-Informed Neural Network (PINN). The two solutions are compared to assess the accuracy of the neural network approximation. We further develop geodesic spike diagrams and surface visualizations to illustrate the deformation of geodesic spheres relative to their Euclidean counterparts. Intrinsic Riemannian surface area and volume are estimated numerically using the induced metric and the Riemannian volume density, respectively. For the chosen metric and a geodesic ball of radius one, the computed area and volume are approximately and smaller than the corresponding Euclidean values at the base grid resolution. A grid-refinement study is also performed to examine the sensitivity of these estimates to numerical resolution. The proposed framework demonstrates how symbolic differential geometry, numerical integration, and PINNs can be combined to investigate and visualize geometric structures associated with Riemannian metrics.
math.NA
Electrical impedance tomography (EIT) reconstructs the conductivity inside an object from voltage and current measurements on its boundary. The resulting inverse problem is nonlinear and severely ill-posed. Neural networks offer a flexible computational approach, but training physics informed neural networks for EIT and relating their training loss to reconstruction accuracy remain challenging. We develop a novel constrained neural stream function method for planar EIT with Lipschitz conductivities. The method builds the conductivity constraints and prescribed boundary voltages into the neural trial functions and replaces the second order conductivity equation with a first order system in strong form. The measured current is also used to construct a fixed baseline for the stream function. For this formulation, we derive error estimates that relate the sampled neural objective to errors in the physical boundary currents and the reconstructed conductivity. The error estimates separate the contributions from neural approximation, measurement noise, and sampling. Numerical experiments further demonstrate that the proposed method achieves high reconstruction accuracy with both exact and noisy boundary data.
stat.ML
Quickest detection problems (QDPs) arise in a wide range of applications. However, the complementarity structure of the associated variational inequalities poses substantial challenges for traditional numerical methods, particularly in high-dimensional settings. We propose a PINN-based framework for estimating the optimal stopping boundary in QDPs with high-dimensional diffusion processes and spatial dependence, while overcoming the curse of dimensionality. Theoretically, we establish a novel equivalence between the free-boundary PDE and an infinite-dimensional stochastic optimization problem, rigorously justifying the use of finite-dimensional neural networks to approximate the true solution. Furthermore, we assess the robustness of the proposed framework by quantifying uncertainty in the learned stopping boundaries using deep ensembles and Monte Carlo dropout. The results show low variability across independent training runs and stochastic forward passes, indicating stable and consistent boundary estimates. We also compare our PINN results with reference numerical solutions where available and find close agreement.