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.
4,558 papers in Physics-informed · newest first
cs.LG
We present a variational functional neural network (vfNN) algorithm that optimizes physically motivated continuum functionals in integral form (e.g., Lagrangian, Hamiltonian, or free energy) to find the states of a system. That way, vfNN bypasses solving the equations of motion (a.k.a. the Euler-Lagrange equations), which are in the form of differential equations. To this end, our approach is fundamentally different from conventional physics-informed neural networks (PINN) that solve differential equations by minimizing a phenomenological loss function involving higher order derivatives and ad hoc weight factors. In contrast, vfNN merely evaluates lower order derivatives of the generating functional and replaces the weight factors with rigorous physical scales. This also fundamentally changes the loss landscape, and the desired solutions may become unstable. For this emergent nonconvex optimization problem, we develop a quasi-Newton optimization algorithm with simulated annealing that converges to the solutions of the corresponding Euler-Lagrange equations of the functional regardless of their stability properties. Our simulations using vfNN give accurate results for benchmark systems governed by linear or nonlinear ordinary differential equations.
physics.comp-ph
The shear piezoelectric coefficient governs the shear-mode electromechanical coupling in piezoelectric micromachined ultrasonic transducers (PMUTs) and surface acoustic wave (SAW) devices, but measuring it typically requires destructive resonance testing on dedicated specimens. On simulated data, can instead be recovered non-destructively from sparse, noisy subsurface wavefield observations using a constrained physics-informed neural network (PINN). By building exact spatial distance functions and temporal multipliers directly into the network output, the clamped, grounded boundaries and resting initial state hold automatically, leaving the loss with only the interior equations of coupled electro-elastodynamics and the data misfit. Non-dimensional scaling brings all governing coefficients within one decade of O(1), and the setup removes the boundary and initial-condition penalty weights that soft-constraint methods must tune. In a six-way comparison (plane-strain PZT-5H, manufactured wavefield, 30 dB noise), a soft-penalty baseline with adaptive weights converges to an erroneous in four of the five runs (51.7% mean error), and fixed penalties reach an error of 0.85% only after a second-order optimization stage. The constrained formulations reach mean errors between 0.15% and 0.51% with held-out displacement errors below 1%. Within these variants, the spatial multiplier gives rapid first-order convergence, and the quadratic temporal multiplier lowers the early-time electrostatic residual by a factor of 6.8 versus a linear one. On finite-element data along one subsurface line, the full formulation recovers with 1.19% mean error at 30 dB and keeps it between 0.65% and 2.71% across a 40 to 0 dB noise sweep. Finally, training on displacements alone still recovers with mean errors of 0.45% on finite-element and 1.64% on manufactured data.
astro-ph.GA
Recent high-sensitivity and high-resolution surveys of the Third Galactic Quadrant [ and ], such as the Milky Way Imaging Scroll Painting ( MWISP) survey, have revealed a significant population of molecular clouds (MCs) that appear virially unbound () according to traditional isolated MC models. However, these apparently unstable cloud structures are actually found long-lived and actively undertaking star formation. This inconsistency presents a Virial Paradox. In the present work, we employ a Physics-Informed Neural Network (PINN) to address this discrepancy by re-evaluating the stability of 2,091 MCs . Unlike traditional machine learning, our PINN model embeds the complete Eulerian Virial Theorem including external surface pressure support () directly into the network's loss function. This model autonomously discovers a global Galactic pressure field that scales inversely with vertical height () and Galactocentric radius (), consistent with the properties of the Galactic Flare. By incorporating this AI-derived pressure support, we demonstrate a dramatic shift in the stability census: 99.9% of previously thought unbound clouds are found to be in a state of pressure confined equilibrium (). Furthermore, we find a robust log-log correlation () between our corrected stability parameter and the star formation rate (SFR). This correlation provides independent physical validation that environmental confinement is a primary regulator of star forming efficiency in the outer Galaxy.
math.NA
Kernel collocation is a meshfree method for partial differential equations whose accuracy depends on the smoothness of the kernel and of the solution. For globally supported kernels, however, the collocation matrices are dense and severely ill-conditioned. We address both issues by combining a multiscale collocation scheme with samplets, a multiresolution basis of discrete signed measures with vanishing moments. In the samplet basis, the collocation matrix has only O(N log N) relevant entries, while the multiscale scheme adapts the kernel width to the spacing of the points on every level. Since the differential operator scales the equations at the interior points differently from those at the boundary points, the rescaling alone does not bound the condition number of the level systems. We therefore solve them by a Schur-complement reduction that is invariant under this scaling. For noisy data, we consider physics-informed kernel learning, which replaces the collocation system by a regularized least-squares fit. We show that it reduces to collocation as the regularization vanishes, and we solve it by a deflated conjugate gradient method that reuses the Schur-complement reduction. Numerical experiments in two and three dimensions, with exact and noisy boundary data, show that the method handles significantly more points than dense collocation.
math.NA
Convection-diffusion equations are fundamental models for transport phenomena, but their numerical solution becomes challenging in convection-dominated regimes due to steep gradients and sharp boundary layers. This motivates the development of accurate approaches capable of effectively resolving such features while avoiding costly iterative optimization. In this study, a modified ELM framework based on shifted Legendre polynomials is developed for convection-diffusion equations in steady-state, continuous-time, and discrete-time formulations. The proposed approach is evaluated on steady and unsteady benchmark problems with relatively high Peclet numbers, including continuous and discontinuous boundary conditions. Finite element method solutions are used as independent solution references. By exploiting the linearity of the governing equations, MELM determines the output weights through a single least-squares solve, avoiding the iterative gradient-based training required by PINNs. The shifted Legendre polynomial basis provides an effective spectral representation for resolving steep gradients and sharp boundary layers. For the DT-MELM formulation, the coefficient matrix remains unchanged across successive time levels, allowing its LU or QR factorization to be computed once and reused. A systematic comparison with PINNs that incorporate advanced training strategies demonstrates that MELM provides higher accuracy and shorter solution times for steady-state and DT-MELM formulations across the benchmark problems considered. In contrast, CT-MELM exhibits scalability limitations as the size of the space–time basis increases. Overall, the results demonstrate the effectiveness of MELM for steady-state and discrete-time convection–diffusion problems, while also showing that PINNs provide better scalability for large space–time formulations where global CT-MELM becomes computationally demanding.
physics.optics
A film-thickness error of 8 nm, within the tolerance of commercial thin-film lithium niobate wafers, shifts the group-velocity dispersion at 1550 nm by about 28 ps km. We study numerically whether a segmented, non-volatile phase-change cladding can correct this error after fabrication. In mode solves of 3012 geometries, SbS switches by a median of 181 ps km at a 40 nm strip thickness with no material absorption under the adopted optical constants, whereas SbSe reaches a comparable contrast at a median modal loss of 5.6 dB cm. Because phase adds along the guide, four independently switched binary segments reach a two-dimensional region of the plane; eigenmode expansion supports this description at the junctions. Full-wave solves at 65 die geometries show that the segment states move with the die error, so the bit pattern is chosen from a per-die model: a spectral surrogate constrained by exact identities of the lossless Maxwell problem. Its accuracy within the training domain is similar to that of unconstrained baselines; it keeps and consistent, and its error at an unseen film thickness is 8.3 rather than 13.0 ps km. With a bare test ring and a second ring carrying a crystalline strip already on the mask, 96.8% of the dies are trimmed into ps km, scored on full-wave solutions. A thermal model gives a candidate write window for a 532 nm beam.
math-ph
Current methods of deriving ultrastiff isotropic metamaterials require heuristics or topology optimization, which are highly inefficient and limited by human input. To circumvent this, Physics Informed Neural Networks are applied to analytical equations to systematically solve for plate orientations in closed cell lattices. Following a standardized procedure, the plate orientations were modelled and assembled into geometries resembling quasi random foams for validation via finite element simulations. Closed cell 6-plate geometries were also additively manufactured using LAPIS and experimentally characterized. The results indicate that a minimum of 6 plates is required to constitute an ultrastiff isotropic lattice, 7 plates would return the established plate Cubic Octet structure while 8 to 10 plate geometries did not show significant differences in properties. Despite the introduction of some plate bending due to sub-optimal plate placement strategy, relative stiffness of the PINNs lattices adheres closely to the Hashin Shtrikman upper bound, 90 percent of Hashin Shtrikman upper bound at a relative density of 0.4, and the lattices maintain near isotropic behaviour, achieving a Zener ratio of 0.95 at a relative density of 0.1. Benchmarking results show that specific stiffness of PINNs lattices is higher than the majority of isotropic architectures reported in the literature.
gr-qc
We develop and validate a physics-informed neural network (PINN) framework for computing the tidal Love numbers of black holes directly from their perturbation equations. We consider static perturbations of the Kerr black hole, whose exact hypergeometric solutions provide a controlled benchmark for both the numerical solver and the extraction of the physical response. The framework combines exact enforcement of the horizon boundary conditions with an -Sobolev loss that incorporates derivatives of the differential-equation residual. The Love number is then obtained by extracting the asymptotic coefficients of the learned solution, without using the analytic connection formula. Across the tested scalar, vector, and tensor perturbations, the method recovers the finite dissipative response with relative errors below . Controlled comparisons show that the higher-derivative loss terms improve solution accuracy by orders of magnitude, while independent tests of the extraction procedure distinguish solver errors from errors in recovering the response coefficients. The conservative response, which vanishes analytically, is constrained by the numerical error floor. These results demonstrate that PINNs can accurately compute black-hole tidal response and establish a validated framework for future extensions to frequency-dependent and non-separable perturbation problems.
cs.CV
Background and purpose: We propose PGPI4MR (prior-guided, physics-informed 4D MRI reconstruction), a deep learning method that leverages information from other respiratory phases or a setup scan, the first 30 s of the same scan, to improve 4D MRI reconstruction without extra scan time. Materials and methods: PGPI4MR is an unrolled network that reconstructs 16 respiratory phases from 60, 30, or 15 s of data, and single 3D volumes, each from 0.29-0.49 s of data, using a setup-scan image. The networks were trained once, on other volunteers, and were not retrained for new volunteers. We evaluated PGPI4MR on measured k-space from three datasets: free-breathing MR-linac (1.5T) and abdominal (3T) scans, and thigh scans with cuff compression (1.5T). All methods, including comparative models, received identical samples and were scored similarly. Results: In vivo, PGPI4MR had the lowest held-out error for 4D MRI at every scan time, and its 16 phases were ready a median of 7.5-13 s after the scan on the 2 GPUs tested. Coupling the 16 respiratory phases reduced the error at 60 s by 9.1% compared with reconstructing each phase alone. For sub-second MRI, the error at 0.49 s was 15.5% lower than that of the best comparison method, classical reconstruction toward the same prior, and on the faster GPU, every 0.29 s window was acquired and reconstructed within 0.5 s. Without retraining, PGPI4MR matched the best methods on the 3T abdominal scans but not on the thigh scans; after retraining on thigh data, it reduced the held-out error by 6.6% relative to the best comparison method. Conclusion: Prior information allowed PGPI4MR to reconstruct 4D and sub-second MRI more accurately than compressed sensing and a published 4D network, within seconds and without extra scan time. This could support 4D MRI for treatment planning and 3D motion monitoring during MR-guided radiotherapy.
cs.LG
Conventional space heating systems typically rely on single or sparse fixed-point temperature measurements, overlooking non-uniform indoor temperature distributions, transient thermal dynamics, and occupant-specific comfort requirements. This study explores an occupant-centric control strategy that aims to maintain the desired temperature around the occupant location. Spatially and temporally varying temperature fields, together with occupant mobility, make real-time local temperature estimation challenging. To address this challenge, we propose a control-oriented Physics-Informed Neural Network (PINN) model for indoor temperature-field prediction. Conventional PINNs rely on explicit time inputs and assume consistent temporal patterns across samples, which limits adaptability under variable initial conditions and heating sequences. The proposed model infers temporal dynamics implicitly from spatial coordinates and limited sensor measurements, improving robustness to changes in initial conditions and external disturbances. The method was validated across nine horizontal sensing planes in three controlled room-scale configurations. Against a validated COMSOL Multiphysics simulation, the PINN predicted the evaluated temperature fields with a maximum relative error below 1.85% across validation cases. These predictions supported an occupant-centric space heating control scheme. Compared with COMSOL-based offline control, the PINN-based system achieved an average prediction error of around 0.67%, and its rapid inference supports real-time occupant-centric control implementation. This work represents a move away from reliance on fixed-point temperature measurements in space heating control to an occupant-centric control strategy informed by real-time environmental feedback.
cs.LG
Physics-informed generative models should produce samples that are both data-aligned and physically valid, yet existing methods are often iterative and too slow for practical use. Achieving this with a one-step flow-map model is difficult because both data-distribution and physics-constraint learning are enforced only indirectly through surrogate objectives, making their joint learning fragile for long-range flow maps. We propose \textbf{Physics-Informed Long-Short Flow Maps with Direct Guidance (LSFM-DG)}, which makes direct target computation feasible by decomposing one-step generation into a long flow map for global evolution and a near-terminal short flow map with computable closed-form solutions and physics potentials. As the short flow map shrinks to zero, it provides both direct distributional and physical targets for learning the long flow map. This yields a unified one-step flow-map model that removes Jensen's gap, improves training stability, and achieves stronger data fidelity and physical consistency without distillation.
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.
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.