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.OC
Antennas come in various shapes and sizes, as their performance characteristics are very much dependent on their exact shape. Coming up with a shape that matches desired design characteristics has, up until this moment, been largely the domain of metaheuristics and local optimization methods. While these methods are convenient, they generally provide no performance guarantees and rarely allow to enforce hard design constraints. In this paper, we show how Mixed-Integer Programming (MIP) can be used to optimize the shape of so-called patch antennas. The methodological focus is to show how underlying laws of physics allow to derive effective bounds on variables as well as new cutting planes. These greatly improve the effectiveness of the underlying basic MIP model, enabling the automated design of practically relevant patch antennas for a wide variety of applications.
eess.IV
Purpose: To mitigate parameter degeneracy and improve robustness of IVIM fitting, a multimodal physics-informed neural network was developed to leverage anatomical information through the combined use of cross attention, selective spatial gating, and anatomy-weighted spatial prior. Methods: T1w and FLAIR anatomical images were co-registered to IVIM signal in native space and segmented by tissue type. The proposed Physics-Anchored Cross-attention Embedding network (PACE) encoded IVIM signals and their anatomical features in parallel branches, then integrated them via cross attention and spatial gating. An anatomy-weighted spatial prior further constrained signal reconstruction using anatomically similar neighboring voxels. PACE and its prior-guided variant were compared with two baseline deep neural networks (DNN and IVIM3C), least squares, non-negative least squares, and maximum a posteriori fitting models. All models were evaluated on signal and parameter reconstruction accuracy and lesion contrast fidelity using data generated from subjects drawn from the University of Rochester COVID cohort. Results: PACE variants demonstrated lower RMSE for all IVIM parameters except for Dmv. The anatomy-weighted spatial prior further reduced RMSE across all five parameters relative to the default PACE, with modest reductions in lesion contrast accuracy for fmv and fint. For in-vivo evaluation, PACE with spatial prior also showed the best signal reconstruction across all noise levels while maintaining good to excellent ICC. Conclusion: Multimodal anatomical information improved IVIM fitting accuracy and robustness, with selective spatial integration via cross attention, gating, and anatomy-weighted spatial prior. Keywords: intravoxel incoherent motion, physics-informed deep learning, diffusion MRI, multimodality fusion, attention mechanism
cs.LG
Neuro-spectral architectures (NeuSA) are a class of physics-informed neural networks (PINNs) that have proven effective for solving time-dependent PDEs in the frequency domain. However, training and inference often rely on costly numerical integration of the learned vector field, typically using sequential Runge-Kutta time stepping, which limits temporal parallelism. We introduce PaPi, an integration scheme inspired by weakly nonlinear flows that enables time-Parallel inference through exponential integration and a Duhamel-Picard scheme. We show that the Duhamel-Picard iteration converges exponentially for all flows, and provide explicit error bounds that depend on how close the flow is to linear. Experiments show that PaPi accelerates training and inference by up to two orders of magnitude, achieving training times of under one second for low-dimensional PDE learning problems, while maintaining competitive predictive accuracy.
cs.LG
Physics-informed neural networks (PINNs) supervise on the residual of a known differential operator. Many high-stakes inference problems admit no such operator: clinical signals, behavioral measurements, materials properties. We introduce the Manifold-Informed Neural Network (MINN), a PINN-parallel paradigm that replaces the physics operator residual with a manifold operator residual: a discrete Poisson equation on a -nearest-neighbor graph in the learned latent space, with a learned, task-aware source. The construction is a structural parallel to PINNs (squared operator residual plus label data, in place of operator residual plus boundary data); the limit recovers the homogeneous Laplace equation (classical manifold regularization solves the same equation but minimizes the Dirichlet energy , a different penalty form). The source takes input features and auxiliary metadata directly, breaking the homogeneous smoothness prior that limits classical Laplacian penalties; gated Feature-wise Linear Modulation separately fuses metadata into the prediction branch. We evaluate MINN on three-class classification of potassium, calcium, and magnesium from 12-lead ECGs in MIMIC-IV-ECG, against twelve baselines spanning supervised and tabular methods, ECG foundation models, and manifold/graph approaches. MINN attains the highest K Macro-F1 of 0.61 (best baseline 0.55), with consistent gains on Ca and Mg and a 31% relative improvement at 1% labeled data. Six targeted ablations show that the inhomogeneous Poisson formulation, not graph smoothing alone, drives the gain.
physics.geo-ph
Rapid and accurate hypocenter determination based on three-dimensional (3D) seismic velocity models is essential for seismic monitoring in subduction zones, yet it remains computationally demanding. HypoNet Nankai, a hypocenter determination package that uses physics-informed neural network (PINN) travel-time inference for a realistic 3D P-wave velocity model of the Nankai Trough subduction zone, was designed to address this problem, but supported only P-wave arrival times. Here, we present HypoNet Nankai PS, which extends the framework to both P- and S-wave travel times. We first constructed an S-wave velocity model from the existing P-wave model using empirical conversion relations for marine sediments and the crust. Because the resulting S-wave velocity structure has lower velocities and therefore considerably steeper travel-time gradients, the original PINN training procedure designed for the P-wave velocity structure was insufficient. We therefore revised the training procedure by reconsidering the distribution of collocation points, the NN architecture, and the optimizer. Benchmark comparisons with the fast marching method showed that the revised approach substantially reduced the root-mean-square deviations for both P- and S-waves compared with the original algorithm. Recovery tests using synthetic earthquakes were also performed. When applied to 223 earthquakes recorded by DONET stations off the Kii Peninsula, the system yielded hypocenters generally consistent with the JMA catalog beneath the network, suggesting that the 3D velocity model captures travel-time variations accommodated by JMA's 1D model and station corrections. Farther seaward, the estimated hypocenters were substantially shallower than those in the JMA catalog and were located in the oceanic crust and uppermost mantle, consistent with previous relocations that used DONET data and 3D velocity models.
math.NA
We develop and compare enhanced neural-network solvers for one-dimensional ground-state profiles, which are solutions of the stationary profile equation for the nonlinear Schrödinger, generalized Korteweg-de Vries, and nonlinear Klein-Gordon equations. Its explicit sech-type solutions serve as exact reference for error computation and benchmark hyperparameter selection. We improve on the standard Adam-trained physics-informed neural network (PINN) baseline by introducing higher-order optimization via Gauss-Newton/Levenberg-Marquardt and L-BFGS refinements, as well as Fourier-feature PINNs, and constrained Deep Ritz (DR) formulations. In DR approaches we introduce two new neural-network formulations, which implement two classical variational characterizations: a Nehari-constrained Deep Ritz method, in which the height is learned by projecting onto the Nehari/Pokhozhaev manifold, and a Weinstein Deep Ritz method, in which a normalized profile minimizes the Weinstein quotient. The Deep Ritz formulations perform best overall, in particular, the Weinstein variant gives the best error-runtime balance. The neural-network based solvers remain less accurate and efficient than classical Petviashvili iteration in 1D, however, the current study provides a proof of concept: the mesh-free formulation, non-reliance on exact profiles or the related features make them promising in higher dimensions and for more complicated nonlinearities and dispersive operators.
math.NA
Physics-informed neural networks (PINNs) and other residual-trained solvers judge a candidate solution by the size of its sampled PDE residual. For first-order Hamilton-Jacobi equations this is not sufficient: the same equation and boundary data admit Lipschitz almost-everywhere solutions that differ from the viscosity solution by while violating the equation only on sets of measure zero. We study whether residual minimization selects such solutions in a fixed-horizon pursuit-evasion game whose Hamilton-Jacobi-Isaacs value function is known in closed form on the circle and on the flat tori and . We train four neural parameterizations with ten seeds on each geometry, 120 runs in total. A standard network with periodic Fourier features converges to folded almost-everywhere solutions in all 30 runs: small residuals and the expected capture-layer gradient, yet values that are wrong over most of the domain. A network with periodicity imposed through the loss recovers the viscosity solution in one and two dimensions but becomes unreliable in four. Two parameterizations that receive the geodesic distance do substantially better: a single network fed the wrapped displacement and its distance recovers the viscosity solution in all 30 runs, while a minimum over periodic image charts succeeds in 27 of 30 and introduces a wrong-image failure mode. Finally, for the convex Hamiltonian considered here, we use the semiconcavity of the viscosity solution to build a mesh-free finite-difference test that needs only forward network evaluations; it detects the folded solutions and the harmful min-of-charts failures without access to the exact value function. A small sampled residual thus does not by itself validate a learned Hamilton-Jacobi solution; the parameterization and independent structural diagnostics can be essential for selecting the viscosity solution.
gr-qc
We present Pinndorama, a physics-informed neural network (PINN) code for solving the Hamiltonian constraint in the puncture formalism. The networks are trained solely on the governing equation and boundary conditions, without an analytical or perturbative guiding solution, with collocation points sampled in curvilinear coordinates. Training combines two optimization algorithms: an initial stage using adaptive moment estimation (Adam), followed by the self-scaled Broyden quasi-Newton method. We apply this approach to a spherically symmetric test problem with a known exact solution, axisymmetric binary punctures with unequal spins, and a fully three-dimensional GW150914-like configuration with unequal spins and orbital momenta. Comparisons with the NRPyElliptic solver yield relative errors of order in axisymmetry and in three dimensions. In addition, we reduce the hyperbolic-relaxation time in NRPyElliptic by a factor of approximately by training a parametric network that takes the puncture spin as input and provides a physics-informed initial guess to the solver. These results demonstrate that PINNs can provide accurate binary-puncture initial data and complement conventional elliptic solvers in numerical relativity.
physics.comp-ph
High-accuracy computation of nonsmooth dynamics is a challenging problem in systems with multiple frictional contacts. This study proposes a general physics-informed neural network framework, termed the mixed leading variable physics-informed neural network (MLV-PINN). By using the governing equations and contact-friction laws as physical constraints, this framework provides common solution approaches for computing nonsmooth dynamics not only in discrete systems but also in continuum systems. Specifically, the network represents accelerations, normal contact forces and friction margins as independent outputs and determines them simultaneously, without first reducing the dynamics to discrete velocity-impulse complementary subproblems. A composite physics-informed loss is constructed from the equations of motion in their original form, contact-friction complementary conditions and a friction-margin consistency relation. To improve stick-slip state identification during PINN optimisation, a mixed leading variable combining relative tangential velocity and acceleration is introduced to reformulate the tangential complementary conditions. Four benchmark simulations cover one-dimensional (1-D) nonsmooth dynamics involving single-contact stick-slip, 1-D nonsmooth dynamics involving multi-contact stick-slip, two-dimensional (2-D) nonsmooth dynamics with coupled normal contact-separation and tangential stick-slip, and 2-D nonsmooth dynamics in a continuum system involving moving contact on an elastic beam. Benchmark comparisons show substantial reductions in displacement and velocity errors relative to the corresponding conventional methods at large time steps. These results, together with an ablation study and tests involving friction-velocity slopes, long-time integration and loss weights, illustrate the computational accuracy and support the broad applicability of the proposed framework.
physics.flu-dyn
Scientific machine learning provides a promising framework for solving complex problems in science and engineering. Notably, physics informed neural networks (PINNs) have shown considerable potential for solving differential equations and modelling engineering systems. Solving time fractional Navier Stokes equations (TFNSEs) on complex domains is challenging due to temporal nonlocality, nonlinear flow dynamics, geometric complexity, and incompressibility constraints. To address these challenges, we propose a geometry gated, divergence-free Gaussian radial basis function Kolmogorov Arnold network (GeoDiv KAN). The proposed architecture uses geometry dependent feature gating and a streamfunction formulation to preserve incompressibility by construction. GeoDiv KAN is evaluated for the time fractional incompressible Navier-Stokes equations on square, circular, and star-shaped domains. Numerical experiments show that GeoDiv KAN achieves higher predictive accuracy than PINN, PIKAN, RBF KAN, and DF RBFKAN across the considered benchmark problems. To establish practical relevance, GeoDiv KAN is applied to two data driven CFD cases: unsteady flow past a circular cylinder using the \href{https://doi.org/10.5281/zenodo.5039610}{Zenodo dataset} and turbulent RANS flow through a complex U bend using the \href{https://huggingface.co/datasets/JDecke/ubend-cfd}{U-bend dataset}.
math.NA
Solutions of second-order elliptic PDE problems on nonconvex or cracked domains with mixed Dirichlet-Neumann conditions typically lie outside . Near re-entrant corners, crack tips and points where the boundary condition changes type, the gradient grows like with . We study residual-based adaptive refinement in hybrid variational-collocation PINNs. A multiscale Fourier-feature network is trained on a composite loss. The loss combines a variational residual tested against Legendre bubble functions, a strong-form collocation term and penalties for the Dirichlet and Neumann data. The variational term needs only first derivatives of the network, whereas the collocation term requires second derivatives and provides a residual that can be evaluated at any point. After each training stage, candidate points selected by this residual are added to the collocation set. The method is tested on five two dimensional benchmarks, namely a Mode~III crack, a cross-shaped domain with four re-entrant corners with unequal amplitude, a reaction-diffusion problem with four localized peaks, a monotone semilinear problem with a boundary layer and the Motz problem. Compared with uniform point insertion under the same collocation and iteration budget, residual-based refinement reduced the relative error by up to a factor of , the relative error by up to a factor of and the relative semi-norm error by up to a factor of .
math.NA
Integrating physical conservation laws into deep neural architectures remains a central SciML challenge. Soft-penalty approaches, including many PINNs, may be sensitive to loss weighting and optimization; generic DEQ and implicit-layer solvers may require instance-dependent iteration counts. We study a norm-linearization scheme for networked systems with linear continuity constraints and nonlinear quadratic or power-law energy balances. We derive sharp universal and finite- bounds on relative variance and, via the weighted Kantorovich inequality, relate them to worst-case single-step squared-norm distortion when target and operating states have a bounded multiplicative ratio. Euler's theorem shows that the scheme is Newton's method for degree-one norm differences . Recasting raw degree- balances as norm differences removes radial curvature, yields a degree-zero homogeneous Jacobian, eliminates the affine Newton term, and row-equilibrates the loop Jacobian at equilibrium. Under regularity and nonsingularity assumptions, this gives local quadratic convergence for Darcy-Weisbach () and Hazen-Williams () models. We implement dynamic sign partitioning in a FlowDEQ layer using a reduced incidence matrix and implicit-function adjoint differentiation.
cs.LG
Kolmogorov-Arnold Networks (KANs) replace fixed scalar weights by learnable univariate maps, yet most spectral KANs still rely on Chebyshev polynomials that live on a bounded interval and therefore require a saturating squashing of the pre-activation. We introduce the Fractional Hermite Kolmogorov-Arnold Network (FHKAN), a neural architecture that equips KANs with an adaptive, trainable fractional-order generalized Hermite basis. With a nonnegative shape parameter, the underlying generalized Hermite functions are orthonormal on the entire real line and uniformly bounded under a Gaussian envelope, so they act directly on unbounded pre-activations without any saturating map. We derive closed-form derivatives of the generalized, fractional, and scaled basis away from the origin and determine its order of differentiability at the origin, where the fractional power map creates a singular point. On synthetic regression, FHKAN attains the lowest test error at every network depth among nine fixed activations and the spline-based KAN. On image classification, image denoising, and sentiment analysis, the best-performing fractional Hermite block yields the highest accuracy or reconstruction quality. On physics-informed problems, FHKAN reaches mean absolute errors of order 10^-6 to 10^-5 on the Lane-Emden equation, residuals of order 10^-4 on the Burgers equation, and absolute errors below 10^-4 on a fractional delay differential equation.
cs.AI
Meteorological downscaling is crucial for high-resolution regional climate forecasting and disaster early warning. While neural operators have emerged as a promising paradigm for modeling complex spatiotemporal mappings, existing frameworks often struggle with spherical manifold geometric distortions, inherent atmospheric multi-scale coupling mismatches, and lack of explicit atmospheric laws. We propose the Spherical Physics-informed Neural Operator, which utilizes a Spherical Laplacian Decomposition to partition atmospheric fields into hierarchical frequency components, maintaining exact point-wise correspondence across scales. To evaluate these representations at arbitrary locations, we introduce a localized spherical integral operator that approximates continuous kernel transforms via geometry-aware attention. Dynamical consistency is further enforced by embedding differentiable constraints into the learning process. Extensive experiments demonstrate that our framework attains superior accuracy and zero-shot generalization across various meteorological variables and unseen queries, representing a robust and interpretable solution for global-to-regional meteorological downscaling.
eess.SY
Understanding how a particular automated vehicle reacts to nearby traffic can improve motion prediction, control development, traffic simulation, and safety evaluation. However, commercial automated driving systems are proprietary, and single encounters may provide only a few seconds of noisy data. Standard physical models are interpretable but inflexible, whereas neural models are often data-hungry. We propose a physics-informed Koopman framework that combines a calibrated car-following law with a correction learned from the observations. A weak-form estimator learns this correction from velocity measurements integrated over time, avoiding noise-sensitive numerical differentiation. The resulting continuous-time model predicts the follower's response and provides interpretable measures of driving behavior. Experiments on OpenACC and CATS-CF evaluate 5-, 7-, and 11-second histories. Averaged over these histories, the constant-time-headway branch reduces speed prediction error by 16.0% and 15.4% on OpenACC and CATS-CF, respectively, relative to the best neural baselines. The PI-Koopman branches achieve the lowest mean speed and gap errors among the physical and neural comparators. Weak-form estimation reduces acceleration-field reconstruction error by 74.5% in noisy known-law simulations and noise-induced field perturbation by 91.6% in paired real-vehicle measurements. The same PI-Koopman system identification supports following-mode recognition with an approximately eleven-fold difference in median residual variance between human drivers and automated vehicles, and a single residual threshold achieves 85.4% balanced accuracy. The branch informed by the intelligent driver model takes a median 17 to 26 ms for identification and forecasting on the tested central processing units, supporting frequent target adaptation.
eess.SP
Recent advances in chemical computing create new opportunities to realize biocompatible communication devices for application in precision medicine. Implanted microscopic transmitters and receivers can exchange information using molecules that diffuse through a biological medium, enabling them to form a network and jointly coordinate sensing and actuation operations. However, randomness in molecular propagation causes severe signal distortion, and receivers have limited computational capacity to compensate. The receiver design must therefore combine robustness to diffusion-induced distortion with computational architectures amenable to implementation in the chemical domain. To meet these requirements, we propose a physics-informed reinforcement learning (RL) framework implemented with the reservoir computing (RC) architecture. We study the task of synchronizing the receiver's clock with a sequence transmitted through a molecular communication (MC) channel. The physics part approximates the maximum-likelihood function synchronization objective, while the other learns a timing policy using this objective as its reward. Simulation results yield clock misalignments above half a second, compatible with molecular transmissions operating on the timescale of seconds.
physics.ins-det
Accurate reconstruction of magnetic fields and their gradients is essential for assessing and controlling systematic effects in precision measurement experiments. We have developed a physics-informed neural network (PINN) method which reconstructs three-dimensional magnetic fields subject to the source-free Maxwell equations, and . In an extension of our previous work on PINN methods for reconstruction of magnetic fields in inaccessible interior regions via measurements at exterior locations, we now demonstrate the feasibility of applying PINN methods to the extraction of magnetic field gradient terms from discrete measurement points subject to constraints from Maxwell's equations.
hep-ph
Extracting generalized parton distributions (GPDs) from experimental observables, the convolution structures denoted as Compton form factors (CFFs), requires solving an intrinsic inverse problem. We presented results using NNGPD, a flexible regression method based on a physics-informed neural-network framework, for reconstructing GPDs using integral constraints – including CFFs and Mellin moments – and symmetry and endpoint constraints. The approach does not require pointwise training information on the underlying GPDs. Closure tests using pseudodata generated from a phenomenological model demonstrate the ability of the framework to reproduce the principal features of the underlying distributions across a range of kinematics. A Bayesian neural-network formulation is also introduced to address uncertainties associated with the reconstruction. Finally, we discussed a broader question in GPD phenomenology: whether the complete momentum-fraction dependence of GPDs is necessary to extract physical quantities such as partonic angular momentum. This motivates investigating approaches that infer Mellin moments directly from experimentally constrained CFFs, while quantifying the remaining ambiguities.
physics.comp-ph
The physics-informed neural network (PINN) faces significant challenges when solving compressible multi-medium flows, including the inability to locate interface positions, poor approximation of discontinuities, and difficulty in handling high-pressure-ratio problems between media with large stiffness differences. To address these issues, we propose PINN with Learnable and Physically Consistent Domain Decomposition (PINN-LPCDD), a framework that incorporates the sharp interface method (SIM) into PINNs for solving compressible multi-medium flows. Firstly, we design separate sub-networks for each medium with learnable parameters to automatically learn interface positions, so that the domain decomposition is physically consistent, and the contact discontinuity at the interface is naturally sharp. Secondly, the Euler equations with artificial viscosity are solved to enhance robustness when handling problems involving shock waves. Lastly, the scaling invariance of the Euler equations is exploited to facilitate the solution of high pressure ratio problems. Numerical experiments on air-air, air-helium, air-water, and air-R22 problems demonstrate the acceptable accuracy of the proposed method in simulating multi-medium flows.
physics.flu-dyn
Reconstructing flow fields from sparse and noisy measurements becomes particularly challenging when data are completely absent from dynamically critical regions, such as the vortex-formation region of a wake. Conventional interpolation and numerical reconstruction methods generally require sufficient spatial or boundary information, while physics-informed neural networks (PINNs) can also face difficulties when sparse and noisy observations provide little or no supervision in the region of interest. To address this gap, we propose a Fourier-feature-embedded complex-valued physics-informed convolutional residual network (FCV-PICRN) for sparse, gappy, and noisy flow-field reconstruction. The framework integrates Fourier features for oscillatory and multiscale structures, complex-valued representations for coupled amplitude–phase learning, and convolutional residual blocks constrained by the Navier–Stokes equations. The method is first verified using the Taylor–Green vortex at and then evaluated for the cylinder wake at . Three severe missing-data configurations are imposed in the dynamically sensitive wake: a large hole, a large truncation, and a plus-shaped gap extending in both streamwise and transverse directions. These gaps are further combined with additive Gaussian and multiplicative speckle noise. Despite having no supervised velocity data inside the excluded regions, FCV-PICRN reconstructs velocity, pressure, and vorticity with high structural similarity index (SSIM) and peak signal-to-noise ratio (PSNR), and remains robust under Gaussian noise up to . Finally, for forced two-dimensional Kolmogorov turbulence with Gaussian noise, FCV-PICRN yields lower reconstruction errors than a conventional PINN. These results demonstrate robust physics-informed reconstruction of severely incomplete and noisy flows across laminar and turbulent regimes.