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.
7,943 papers · newest first
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.
cs.CE
Model order reduction has the potential to enable real-time patient-specific assessment of cardiovascular flows. However, it still faces significant challenges stemming from the geometric variability of vascular anatomies. Building upon the SynthAorta dataset (Bosnjak et al., IEEE Trans. Med. Imag. 45(1), 2026) of physiological aortic geometries, we generate an extensive dataset of physiologically consistent computational fluid dynamics solutions through an automatic boundary-condition adjustment procedure. A common reference geometry allows all patient-specific anatomies to be represented by displacement fields, providing point-to-point correspondence without the need for geometric registration. Based on this dataset, we develop Graph U-Net and Transformer U-Net surrogate models to predict velocity and pressure fields at peak systole. We further investigate two strategies to enhance data efficiency and prediction accuracy: active learning and differentiable physical consistency constraints based on the finite element residual. The results show that active learning is strongly regime-dependent: while it offers little benefit over random sampling during early training, it improves performance during fine-tuning through gradient- and subspace-based acquisition strategies. Similarly, physical consistency constraints prove to be substantially more effective as a fine-tuning objective than as a regularizer applied throughout training. Finally, out-of-distribution studies demonstrate that the primary limitation of surrogate models lies in the geometric support of the underlying parametrization rather than in the neural network architectures themselves. The proposed framework combines synthetic dataset generation, geometry-aware surrogate modeling, physics-informed optimization, and active learning into a scalable workflow for inter-patient hemodynamic prediction.
cs.RO
We develop an uncertainty-aware, operator-learning-based surrogate for tendon-driven continuum robots (TDCRs) that generalizes across robot design and actuation while predicting the complete equilibrium configuration. Our central idea is a nonstationary Gaussian-process (GP) kernel whose metric is learned by a shallow neural network from mechanics-aware design coordinates. The network learns how similarity changes across design space, while the resulting kernel defines the design-to-pose operator, its posterior uncertainty, and a criterion for sequential simulator acquisition. We represent backbone position and rotational strain with spatial kernels and reconstruct orientation directly on SO(3), preserving valid material frames and tendon geometry. We use ASkotch with Nystrom preconditioning for scalable kernel operator solves and a separate Nystrom approximation for posterior covariance. Experiments show that kernel-coverage acquisition reduces mean trajectory error by approximately 15% relative to IID sampling, while posterior variance increases for increasingly unsupported designs. Compared with prior neural-operator TDCR models, the method is 30-50% more accurate using approximately 5x fewer training designs while additionally providing posterior uncertainty estimates.
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}.
eess.SY
The continuous evolution of next-generation power systems, characterized by the high penetration of renewable energy resources and dynamic topology variations, poses formidable challenges to traditional N-1/N-2 contingency analysis in terms of computational efficiency and scalability. While deep learning-based methods offer accelerated inference, existing studies predominantly treat contingency analysis as a pure regression problem, often overlooking the physical essence of grid operation and engineering requirements of real-world scenarios. To bridge this gap, this paper proposes a physics and prompt-guided graph foundation model (PhyPro-FM) for generalizable and engineering-viable contingency analysis. The proposed architecture integrates graph neural networks with a learnable global query mechanism and, notably, introduces a prompt-guided learning paradigm. By leveraging historical snapshots as few-shot prompts, the model dynamically captures correlations between target and historical operating conditions, significantly enhancing generalization capabilities under unseen topologies. Furthermore, we design a physics-informed training mechanism that prioritizes branch power flow errors over nodal voltage errors, aligning the optimization objective with critical grid security constraints. To ensure engineering applicability, a physics-informed inference mechanism is also developed, incorporating a residual-based correction module and a specialized post-processing strategy for singular branches to circumvent numerical instability. Comprehensive experiments demonstrate that PhyPro-FM outperforms state-of-the-art methods in accuracy and generalization, validating its superior physical consistency and robustness for practical engineering applications.
cs.LG
Neural operators offer an efficient data-driven approach to predicting complex automotive aerodynamic flows. However, spectral bias limits their ability to reconstruct fine-scale flow variations around geometric features such as side mirrors and wheel arches. Reliable assessment of local geometric changes therefore requires models that capture fine spatial detail together with global flow interactions. Inspired by iterative refinement and state evolution, we propose CIS-Transolver, a cross-layer incremental-state neural operator that integrates local multiscale information into global flow modeling. The method extracts local feature variations and encodes them as zeroth- to second-order geometric moments. These encodings are combined with information from earlier layers to form a cross-layer memory. Memory-derived corrections enter the value branch of Physics-Attention, allowing local details to inform global physical-state interactions throughout the network. We systematically evaluate CIS-Transolver on three public automotive aerodynamics benchmarks, ShapeNet-Car, AhmedML, and DrivAerNet++, covering surface pressure fields and volumetric pressure and velocity fields. CIS-Transolver achieves the lowest mean relative L2 error among the evaluated methods for all five prediction metrics across the three benchmarks. Relative error reductions average 8.72% compared with the best baseline for each metric. Also achieves the lowest high-frequency spectral errors across all five metrics, with an average relative reduction of 16.06% compared with the best baseline. These results support cross-layer reuse of local information for fine-scale automotive flow prediction.
cs.LG
Surface irrigation planning requires screening many operating conditions and spatial configurations, while high-fidelity shallow-water-equation (SWE) simulations are expensive. We study tabular surrogate models for predicting maximum water height from drone-derived field morphology, terrain, hydrological, spatial, and scenario descriptors, where each row represents a spatial cell under one irrigation scenario. To assess deployment feasibility, we evaluate gradient-boosted trees, neural tabular models, AutoML, and tabular foundation models (TFMs) under two regimes: same-sector generalization, where a model predicts unseen scenarios after observing a limited set of configurations in the same sector, and sector-out transfer, where knowledge learned from source sectors is transferred to an unseen sector. The main findings are twofold: a) under the evaluated fixed 8/32 same-sector split, surrogates achieve strong performance, especially with raw spatial coordinates; b) sector-out transfer is substantially harder because the target sector has different coordinates and geometry. Sector-frame normalization of spatial coordinates improves transfer across similarly structured sectors, but does not solve cross-shape generalization. Overall, tabular surrogates appear useful for same-sector scenario screening under this fixed split, while robust transfer to unseen sectors remains open.
physics.med-ph
Background. The pyriform aperture is a critical anterior bony constriction governing nasal airflow and is clinically relevant to both functional and aesthetic nasal surgery, yet the degree of pyriform aperture enlargement (PAE) needed to capture its aerodynamic benefit is undefined. This study employs high-fidelity computational fluid dynamics (CFD) to quantify the aerodynamic effects of progressive PAE and identify a threshold beyond which further enlargement yields minimal benefit. Methods. A CT-derived three-dimensional nasal airway model was digitally modified to produce baseline, 5%, 10%, 15%, and 20% increases in pyriform aperture cross-sectional area. Pressure-driven large-eddy simulations (LES) were performed at a fixed transnasal pressure difference of 11.25 Pa to quantify changes in inspiratory flow rate, total airway resistance, and local airflow characteristics. Results. Progressive PAE monotonically increased inspiratory flow from 15.063 to 15.252 L/min (approximately 1.25%) and reduced airway resistance from 0.6138 to 0.6028 Pa.min/L (approximately 1.80%). The aerodynamic response was strongly nonlinear, with the greatest improvement occurring between 10% and 15% enlargement. Increasing the aperture from 15% to 20% produced negligible additional improvement. Conclusions. PAE improves nasal airflow by reducing the resistance imposed by the anterior bony constriction. In the anatomical model investigated, approximately 15% area enlargement represented an efficient aerodynamic threshold, after which the dominant resistance shifted toward downstream nasal structures and further enlargement produced little additional benefit. These findings support a conservative, anatomy-dependent approach to PAE and warrant validation across a broader range of patient-specific geometries.
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.
physics.chem-ph
Methyl acetate production via direct carbonylation of dimethyl ether and carbon monoxide involves strong nonlinear interactions among reactor operation, recycle structure, and energy consumption, making conventional simulation-based optimization computationally demanding. In this work, a data-driven framework integrating steady-state process simulation, surrogate modeling, and Bayesian optimization was developed for process intensification. A dataset of 2730 steady-state simulations was generated using a Python-based automated process simulation workflow and a structured design of experiments across the operating domain. Surrogate models were trained to predict carbon conversion yield (C-yield) and cost of specific energy consumption (C-SEC), with neural network-based models showing the best predictive performance and robustness. These models were integrated into a multi-objective Bayesian optimization framework to identify optimal operating regions. Results indicate that high C-yield (up to ~95%) can be achieved with reduced energy cost through lower recycle flow rates and compression demand. Pareto analysis revealed a nonlinear trade-off between C-yield and C-SEC, where further improvements near the conversion limit require disproportionately higher energy input. Validation against rigorous simulations showed deviations below 3% for C-yield and 10% for C-SEC.
cs.AI
Poisson equations frequently appear in various fields, such as mathematics, physics and informatics. Solving Poisson equation, however, is challenging. Traditional methods are not data-specific, although have high certainty. They require a large number of iterations due to the CFL numerical stability. In contrast, deep learning methods are data-driven and more efficient, but require accurate training data and suffer from heavy computation. To tackle these issues, we propose a wavelet-inspired Poisson solver with 24 trainable scalars. The proposed network has several advantages. First, it is compact. It has four independent kernels, each represented by six parameters, leading to 24 scalars in total. Such compact format can be deployed on most devices. Second, thanks to the loop design, it achieves higher accuracy than previous methods. A residual loop reuses the wavelet block without increasing its parameters. Numerical experiments confirm that such loop indeed improves the solving accuracy. On 10000 images, one, two, and three loops of the wavelet block lead to PSNRs of , , and dB, respectively. Third, the proposed method is computationally fast. Thanks to the wavelet transform, the proposed method has linear computation complexity, leading to high computation performance. In short, we propose a novel looped wavelet neural network with compactness, accuracy and efficiency for solving Poisson equations. Our method can be applied in various fields, such as computational fluid dynamics, image reconstruction, biomedical engineering, electromagnetic field simulation.
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.
physics.plasm-ph
Real-time control of tokamak plasmas requires the electron density profile. However, in a reactor-relevant device, diagnostic port access is limited and the profile can be observed only partially. In the present work we reconstruct the density profile by inferring the coefficients of a physics-based one-dimensional particle transport equation, using a Fourier Neural Operator (FNO) surrogate of the transport solver as a fast differentiable forward model. The surrogate enables realtime-compatible gradient-based reconstruction and uncertainty quantification from the reflectometry and interferometry measurements. We compare four uncertainty quantification methods - multi-seed ensembles, the Laplace approximation, Metropolis-Hastings, and a Gaussian method independent of the reconstruction fit. The resulting uncertainty is scored with CRPS and coverage calibration, separately on the observed and unobserved regions. We further demonstrate advantage of our approach over standard analytical function fit on synthetic and experimental DIII-D discharges.
cs.LG
Neural networks whose inputs are functions, as in operator learning, are usually shown to be universal by existence arguments, either by reduction to finite-dimensional networks or by Stone–Weierstrass-type density; these prove that approximants exist but say little about how the parameters depend on the target. We take a constructive route. We extend the ridgelet transform, an integral transform related to the Fourier, Radon, and wavelet transforms, to continuous maps on a separable infinite-dimensional Hilbert space, replacing the Lebesgue measure that is unavailable in infinite dimensions by Gaussian weights with a homogeneous mixture on the direction space. The resulting transform has a Plancherel identity and reconstruction formulas incorporating the frame operator, the correction induced by the weights, and it assigns to each target an explicit coefficient measure, one for every admissible analysis filter. From these representations we obtain uniform approximation on compact sets for all continuous non-polynomial activations of polynomial growth, including ReLU, and, by Monte Carlo sampling of the coefficient, finite-width networks with a dimension-free error in the width for globally Lipschitz activations and coefficients with finite variation and second moments. Explicit examples include Gaussian targets and neural-operator layers. A companion Lean~4 formalization provides machine-checked proofs, with its correspondence to the manuscript documented at https://shosonoda.github.io/lean-operator-ridgelet/ .
quant-ph
Future quantum networks will rely on control-plane decisions such as routing, scheduling, entanglement provisioning, purification, and memory allocation. Each decision depends on a timely and reliable estimate of the quality of the entanglement that a candidate path can deliver, with end-to-end fidelity as a central metric. Inspired by the optical-networking experience with quality-of-transmission (QoT) estimation, this article asks when a quantum controller should compute fidelity analytically, simulate it, or learn a surrogate model. The optical analogy is useful but incomplete: optical QoT estimation often predicts a scalar transmission margin, whereas quantum QoT estimation must account for probabilistic entanglement generation, random memory waiting times, decoherence, state consumption, and measurement constraints that can make fidelity a stochastic target. We propose a compute/simulate/learn framework for quantum QoT estimation and illustrate it with a simulation-based proof of concept. Our study shows that analytical composition can be sufficient in simple regimes, that simulation becomes necessary when stochastic memory effects shape the delivered fidelity distribution, and that lightweight learned surrogates can approximate simulator labels at much lower runtime cost for online control. We close with open challenges for deployment, including stochastic targets, sim-to-real transfer, data-generation cost, physics-informed learning, and generalization beyond individual paths to full network topologies.
cond-mat.dis-nn
We present a transformer-based variational autoregressive network for sampling lattice systems with continuous degrees of freedom and apply it to the two-dimensional XY model near the Berezinskii-Kosterlitz-Thouless transition. The architecture is combined with physics-informed ingredients: locality-informed attention and approximate probabilities. The resulting sampler significantly outperforms existing neural samplers. We train the model on lattices up to , verify with a mode-dropping estimator that no parts of the configuration space are missed, and reproduce the energy, magnetization and helicity modulus obtained with the traditional Markov Chain Monte Carlo algorithm.
eess.SY
We address the problem of improving the performance of pre-stabilized networked systems subject to plug-and-play (PnP) operations, namely additions or removals of subsystems. While distributed baseline controllers can preserve stability after a PnP transition, augmenting them with expressive neural policies can invalidate the formal stability guarantees. To overcome this issue, we build on recently proposed Performance Boosting controllers based on the Internal Model Control (IMC) principle, which reduce closed-loop stability to a finite -gain requirement on an auxiliary operator. In the distributed setting, this operator is formed by interconnecting local neural operators that exchange information only between neighboring subsystems. We then derive free parametrizations of this interconnection, namely explicit maps from unconstrained trainable variables to interconnected neural operators satisfying a prescribed network gain bound for every parameter value. The obtained distributed neural controller can therefore be trained by unconstrained gradient-based optimization without stability constraints or projection steps, while retaining the prescribed gain bound at every training iterate. We develop two complementary parametrizations. A neighbor-based compositional parametrization uses local coupling bounds, so that after a PnP event only subsystems whose bounds change need to update their gain parameters. A network-norm parametrization instead uses a bound on the overall coupling matrix and can reduce conservatism, at the price of requiring network-wide information. A PnP DC-microgrid case study shows that the proposed neural layer improves voltage transients under topology changes and load variations while preserving nominal closed-loop stability.
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.