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.
Neural CFD surrogates, datasets and outlooks we keep coming back to.
Neil Ashton et al. · 2025
Neil Ashton et al. · 2024
Benedikt Alkin et al. · 2025
Rishikesh Ranade et al. · 2025
Corey Adams et al. · 2025
Hang Zhou et al. · 2026
7,940 papers · newest first
cs.LG
Training neural operators on million-cell meshes can exceed GPU memory limits. Models are therefore trained on subsamples and deployed on whole meshes or selected regions. However, subsampling can distort boundary information, degrading accuracy. We ask when boundary conditioning under sampling stays consistent with whole-mesh training, and how to aggregate and inject boundary data. Representing the solution as an integral of boundary data against type-dependent measures, we show that subsampling distorts this conditioning in three ways: incomplete boundary coverage or a sample-dependent global state, face weighting by count rather than area, and compression of boundary inputs into a low-dimensional vector. This analysis yields four measurable consistency conditions checkable before training. We satisfy them with two backbone-agnostic modules. Boundary Quadrature Attention (BQA) aggregates all boundary faces, typed and area-weighted, into slice tokens that every query point reads at every layer. Anchored Global State (AGS) estimates the global state from anchors independent of the sampled points. Adding both to a scalable message-passing and slice-attention backbone yields SCANO. We evaluate the approach on controlled and public benchmarks and a data-centre thermal simulation dataset (DCTS) containing million-cell meshes. On both benchmarks, BQA improves every backbone, reducing whole-mesh error up to 15-fold. On all three datasets, AGS aligns regional with whole-mesh predictions, cutting regional error at least tenfold for most backbones on the public benchmark. Together, the modules nearly halve the best original backbone's whole-mesh error on both benchmarks. SCANO predicts a room-scale field in under one second, over 100 times faster than whole-room anchor self-attention.
cs.LG
This paper presents a CFD dataset of a highly parametrized 3D wing operating in ground effect, designed for benchmarking neural surrogate models for aerodynamic prediction, using a wing shape and flow conditions typically encountered in motorsport applications. The dataset comprises 770 RANS simulations of 194 unique wing configurations, sampled across 27 airfoil profile variants and 4 distances from the ground, spanning variations in wing sweep, chord, taper, angle of attack, and tip twist. Six neural network architectures representing distinct paradigms — convolutional (DoMINO), graph-based (X-MeshGraphNet), transformer-based (AB-UPT, GeoTransolver, GAOT), and JEPA-based (AeroJEPA) — are evaluated on their ability to predict surface pressure coefficient and wall shear stress distributions, from which integral drag and lift coefficients are recovered. The dataset is intended to be used as a challenging benchmark for surrogate CFD models, due to the uniqueness of the ground effect being absent from other wing and airfoil datasets.
cs.CV
Many fields of physical interest on the sphere, such as wind, the polarisation of the cosmic microwave background and the shear of weak gravitational lensing, are spin fields, whose values change phase when the local frame rotates. We extend spherical Fourier neural operators (SFNOs) to fields of any spin, through lifted spherical convolutions that are exactly rotationally equivariant. Lifting spin fields to Mackey functions on the rotation group provides the conceptual framework, while computation is performed exactly and efficiently through their harmonic representation and by appealing to sampling theorems on the sphere and rotation group. We construct spin SFNOs (SFNOs) from these building blocks. We demonstrate empirically that rotational equivariance holds to machine precision for these layers. We achieve state-of-the-art performance on existing benchmarks, and introduce new benchmarks on which spin-aware models outperform their scalar counterparts.
stat.AP
Digital Twins are evolving from passive virtual representations into closed-loop systems that continuously synchronize with physical assets and drive real-time decisions. Yet predictive modeling, machine learning (ML), uncertainty quantification (UQ), and decision-making have been studied as separate capabilities, leaving limited understanding of their integration and maintenance during online operation. This narrative review, scoped by the functional requirements of real-time decision-making rather than by Digital Twin terminology alone, examines how such decisions are generated and sustained in engineering Digital Twins. We first examine foundational decision-making architectures and representative engineering applications, followed by methods that address their limitations across the decision loop. We identify optimization-based, policy-based, and knowledge-based approaches as the major pathways from virtual representation to action. Across them, ML plays three roles in decision-making: enabling efficient surrogate modeling, transforming heterogeneous physical feedback into decision-relevant information, and accelerating or directly generating decisions. UQ supports uncertainty-aware decisions and model adaptation, while continual validation, drift detection, and adaptation help maintain reliable operation as the physical system evolves. Together, these findings underscore the need for a shift from a model-centric to a system-centric perspective on Digital Twins, where its performance depends on the interactions with sensing, state estimation, computation, decision-making, and adaptation rather than on their standalone performance. Therefore, future research should shift from isolated algorithm development toward system-level co-design, scalable decision-making, and approaches to design, and data-efficient continual adaptation and validation for AI-enabled autonomous systems.
cs.LG
Prestress governs the stability, stiffness, and dynamic behavior of tensegrity structures, but it is not directly observable from sparse structural measurements, and it may decrease during service life. Under strong excitation, the cables may slacken and the dynamics become nonsmooth. Existing identification methods are limited to the taut regime, and physics-informed networks for tensegrities solve only the forward problem of predicting the response from known member parameters. This study formulates the inverse problem. Neural networks are trained on the equation-of-motion residual in constrained Cartesian coordinates, where the mass matrix is constant and the force densities enter linearly. The force densities, damping, and axial stiffness are trainable parameters, and the tension-only cable law is kept. A Fisher-information analysis shows, before inversion, which member parameters a record can determine. The method is tested on simulated planar tensegrity frames with up to five modules and a three-dimensional prism, and on measured records of a biomimetic leg and a full-scale tensegrity simplex. On the one-module frame, the identifiable force densities are recovered within 1.5% from noisy accelerations at half the free coordinates, on records with and without taut-slack transitions. Records with transitions determine members that taut records leave undetermined. On the five-module frame, a 16-cable two-span bridge, the median force-density error rises moderately, to 4.2%. On measured records, an identified spring stiffness is within 0.1% of its independently measured value on average, and the identified simplex prestress at 13 levels agrees with its cable force transducers to 2.9% root-mean-square.
cs.LG
Evolution equations with time-dependent coefficients force a neural solver to spend capacity on a scale that the equation already determines. We show that a single classical object, the Ermakov-Pinney scale function , can be written into the input layer of a physics-informed neural network as a parameter-free embedding. One construction covers three problem families through the two signs of the Pinney constant : linear diffusion (, ), diffusion in a time-dependent confining trap (, ), and the quantum oscillator with time-dependent frequency (). An exact moment identity gives in closed form from the initial data alone, so no auxiliary network or knowledge of the solution is needed. Our central finding is comparative: each family requires a different component of the construction and has a different honest control. In family I, the diffusive-time reparametrisation alone reproduces most of the gain, so that family is a poor test of the idea and shows why an ablation is mandatory. In family II no time reparametrisation exists, the control degrades accuracy, and the amplitude prefactor becomes essential (40.8x). In family III the adiabatic approximation also fails, and the quadratic phase factor is what matters (5.7x). The method does not help when the reduced solution does not converge to a fixed point: its extrapolation advantage then disappears. The reduction itself is the classical scaling-variable change of the self-similar-asymptotics literature; what is new is the moment identity that makes it architectural for time-dependent coefficients, and the comparative anatomy above.
cs.LG
Neural operators provide efficient surrogates for computational fluid dynamics (CFD), but most are designed for static geometries and are not equipped to model unsteady flows induced by continuously moving boundaries. We study dynamic-boundary 4D CFD prediction for articulated moving geometries and introduce RoboCFD-4D, a temporally resolved robotic CFD benchmark spanning diverse morphologies and flow conditions. To address the computational and autoregressive challenges of this setting, we propose DynaSolver, a neural operator that explicitly conditions on boundary evolution and causal flow history. DynaSolver employs an efficient physical-token formulation that amortizes point-to-token projection across the operator stack, substantially reducing repeated point-space spatio-temporal computation while retaining accurate point-level reconstruction. We further introduce Replay-Augmented Parallel Training, which exposes the model to autoregressively generated histories while preserving parallel dense supervision, narrowing the gap between ground-truth-conditioned training and autoregressive rollout. Experiments on RoboCFD-4D show that DynaSolver achieves the best full-rollout accuracy among a broad range of learned CFD surrogates, with its advantage increasing as rollout proceeds, indicating substantially reduced autoregressive error accumulation. Project page: https://made-gpt.github.io/DynaSolver-ProjectPage.
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.
physics.comp-ph
Machine-learning surrogates are increasingly proposed to replace phase-field fracture simulations in many-query tasks such as uncertainty quantification, inverse analysis and design. Little controlled evidence shows which architectures are reliable, for which fracture problems and how far beyond their training data. We introduce Fracture-Bench, an open benchmark of two phase-field datasets with fixed splits, common test metrics and a description of each dataset's physical regime. Dataset~1 contains 1,000 AT2 simulations of multiple cracks growing from a notched hole in a hyperelastic plate under random non-uniform biaxial boundary displacements (44 load steps, grid). Dataset~2 contains 4,000 PF-CZM simulations of a pre-cracked plate with two inclusions, each ten times stiffer or more compliant than the matrix ( grid). We train a Fourier neural operator (FNO), DeepONet, Latent DeepONet, a UNet and a conditional diffusion model on identical splits and compare one test metric per dataset, training time, inference time and model size. On Dataset~1, FNO and Latent DeepONet attain mean test errors of order , about ten times lower than UNet and DeepONet. On Dataset~2, the diffusion model is most accurate, with about one sixth of the UNet error, but requires \SI{706}{s} per prediction versus \SI{6}{ms} for UNet. For all architectures, most of the error occurs in the final load steps, after crack localization. Dataset~2 contains initial cracks less than one grid cell apart that produce qualitatively different paths. Architecture rankings therefore depend on the task, and errors averaged over densely sampled inputs reveal little about near-bifurcation cases. Data, codes, splits, regime descriptors and generalization splits are public, with a protocol for adding under-represented regimes such as mixed-mode, three-dimensional and experimentally paired fracture.
cs.LG
Spherical-harmonic neural operators provide an efficient representation for global forecasting, but their discretized pointwise nonlinearities can break rotational equivariance through aliasing. Clebsch-Gordan (CG) tensor products provide exactly equivariant interactions between spherical-harmonic representations, but their computational cost grows rapidly with spectral bandwidth and has limited their use at forecasting scale. We introduce LCG-SFNO, which combines low-rank CG interactions within a controlled low-degree band with coefficient-space residual propagation and an exactly projected quadratic nonlinearity, preserving SO(3) equivariance throughout the learned operator. To make the CG interaction practical, we further develop SSHCG, a sparse GPU implementation with a factorized alternative for wider coupled bands. On spherical shallow-water dynamics and the ERA5-based WeatherBench benchmark, LCG-SFNO reduces rotational error to numerical precision (more than three orders of magnitude below SFNO on shallow water and five orders of magnitude below it on WeatherBench), while matching SFNO on shallow-water forecasting and substantially improving forecast skill relative to SFNO on WeatherBench. Matched ablations show that CG coupling accelerates convergence, while SSHCG keeps the coupling to about 10 percent of a training step at the operating bandwidth, making exact equivariant coupling practical at forecasting scale.
cs.LG
Physically based two-dimensional hydraulic models are too slow for real-time inundation forecasting and large ensembles. We present a time-dependent geometry-informed neural operator (GINO) surrogate of LISFLOOD-FP for the municipality of Forlì (Italy), severely affected by the May 2023 Emilia-Romagna floods. The surrogate is designed for an operational setting in which only river stage gauges and rain gauges are available. A reproducible pipeline turns public regional observations into a physically based training set: each river inflow is driven by the first stage gauge downstream of it through a calibrated water-surface boundary condition, and rain enters as SCS-CN effective rainfall. The surrogate is an autoregressive GINO trained on 216 simulations of 24 observed events with scaled forcing. It predicts volume-conserving polygon-mean depths on an exposure-based Voronoi mesh of 659 nodes, with a 20 min step over 72 h. The surrogate is tested on 38 independent observed events that it never saw during training. On these events it reaches a critical success index (CSI) of 0.934 at 0.05m and 0.844 at 0.3 m, a depth RMSE of 0.008m and an of 0.984 for maximum-depth maps. On one NVIDIA A10G GPU a 72-h forecast takes 1.7 s instead of 55 s with LISFLOOD-FP, and a 50-member ensemble, computed in a single batched rollout, takes 6.2 s instead of about 46 min, which makes probabilistic flood forecasting practical. These results show that neural-operator surrogates can deliver accurate pluvial-fluvial flood forecasts driven by river stage for operational early warning.
astro-ph.CO
Simulation-trained generative models are emerging as a powerful framework for field-level inference in cosmology, particularly in strongly nonlinear regimes where analytical approaches become intractable. However, the finite size of training datasets often leads to variance shrinkage, indicating that part of the realization-level variability of the underlying physical process is not captured by the learned generative dynamics. In this Letter, we interpret variance shrinkage as a diagnostic of missing effective degrees of freedom and introduce physics-informed latent modifications to the generative dynamics of a continuous normalizing flow. We show that these latent corrections recover a substantial fraction of the missing variability without requiring additional training simulations. Using weak-lensing field-level inference as a representative cosmological application, we further demonstrate through posterior analysis that the learned latent directions are actively exploited during inference and behave as effective nuisance parameters that absorb part of the mismatch between the training and target distributions. As a result, the model exhibits improved robustness to out-of-distribution shifts in field-level inference. Our work establishes variance shrinkage as a practical diagnostic for identifying missing degrees of freedom in simulation-trained generative models and provides a framework for recovering them through physics-informed modifications of generative dynamics.
cs.LG
Geometry-aware neural operators face substantial computational and memory demands when learning across complex physical domains. We introduce Architecture-Aware Mixed Precision (AA-MP), a replica-exchange training strategy that allocates numerical precision according to replica roles and architecture-specific operations. By retaining FP32 for refinement while selectively employing BF16 for exploration, AA-MP preserves predictive accuracy while improving training efficiency. Across fluid dynamics and three-dimensional structural mechanics benchmarks, AA-MP achieves comparable accuracy to full-precision training over an ensemble of runs, while reducing hot-replica peak GPU memory by 46.9% and training time by up to 25.8%. It also outperforms naive Automatic Mixed Precision (AMP) in memory efficiency and computational cost, with increasing memory advantages at larger model and geometry scales. Ablation studies show that retaining FP32 in the cold-replica is important for predictive accuracy, while additional FP32 operations in the exploratory replica provide limited benefits relative to their computational cost. Finally, conformal prediction for uncertainty calibration shows that AA-MP achieves near-nominal coverage with narrower prediction intervals than the alternatives. These results advance the scalability of geometry-aware scientific machine learning by reducing computational costs without compromising predictive accuracy or uncertainty quantification.
math.NA
The perfect electric conductor (PEC) boundary condition alone does not eliminate the gradient nullspace of the Maxwell curl-curl operator. Consequently, a boundary-only Maxwell implementation of Eig-PIELM, an eigenvalue extension of the physics-informed extreme learning machine (PIELM), may retain represented gradient modes in its reduced trial space, producing nonphysical, gradient-contaminated modes. We develop dR-Eig-PIELM, a finite-dimensional structure-preserving extension that retains the linear-coefficient, boundary-null-space, and one-shot multimode architecture of Eig-PIELM. It combines compatible tensor-product grad–curl trial spaces with a constrained null-space construction to restrict the sampled PEC space to the mass-orthogonal complement of the represented gradient image before the eigensolve. Symmetric weak-form Gram assembly yields a symmetric-definite reduced eigenproblem without an eigenvalue cutoff under the stated sampling and material-positivity assumptions. For rectangles and cuboids, we establish fixed-degree exactness at the PEC vector-field space and derive rank and dimension identities. Numerical experiments show that dR-Eig-PIELM excludes the spurious eigenmodes with significant gradient components observed in the boundary-only baseline. The method exhibits rapid convergence with increasing polynomial degree and competitive work–precision performance in the tested configurations. A covariantly mapped waveguide example illustrates the potential of dR-Eig-PIELM for integration into design optimization workflows through a constrained local geometry update driven by computed cutoff frequencies and their sensitivities. This work provides a mathematical and computational framework for separating represented gradient modes from physical Maxwell eigenmodes within Eig-PIELM and supports its use in waveguide spectral analysis and geometry design.
cs.LG
Physics-driven design seeks high-performing geometries, which need not conform to a learned shape category. Parametric and latent-space approaches facilitate surrogate-based optimization, but restrict deformations to prescribed shape families or learned decoders. We introduce the Mesh-to-Shell Neural Operator (M2S-NO) as the mesh-to-shell component of a category-agnostic inverse shape optimization framework. We separate the explicit mesh used for design from the volumetric representation used for physics prediction. M2S-NO maps oriented surface samples to a surface-centered shell representation, such as TruncatedSDF or HeatSDF. A separate problem-specific PDE neural operator (PDE-NO) maps this representation to physical fields. Objective gradients update mesh vertices through both operators, without a latent shape decoder. Preconditioning and remeshing support free-form deformation, while fixed interfaces are controlled directly on the mesh. Optional shell-space proposals enable topology changes. We evaluate geometric matching, jet-engine brackets, and neutron moderators, with independent FEM and OpenMC evaluation. Relative to the best training designs, M2S-NO reduces maximum bracket displacement by 14.3% and increases neutron-sensor current by 13.8%. Optimization also succeeds from an out-of-distribution bracket initialization, demonstrating the framework's geometric flexibility.
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.LG
The use of collections of independent local Gaussian processes (GP-ind) combined with trust regions is a widely adopted approach for large-scale and high-dimensional Bayesian optimisation (BO). However, this approach suffers from several limitations, including discontinuities at the boundaries of disjoint regions, an inability to capture long-range spatial correlations, potential information loss, and abrupt increases in computational overhead. To address these limitations, this paper introduces a novel BO algorithm, termed BO-pro-c-tr. The proposed method employs a product-of-experts Gaussian process model with uncertainty calibration (GP-pro-c) as its surrogate model and incorporates a one-to-many association strategy for integrating GP-pro-c with trust regions. Empirical results suggest that, when combined with the GP-LCB acquisition function, BO-pro-c-tr achieves an average reduction of 2.6% in simple regret and 34.9% in computational overhead relative to BO algorithms based on independent local GP models coupled with trust regions.
cs.CV
Prediction errors from video world models are often treated as physical surprise, but they can also reflect appearance, static content, motion, or ordinary prediction difficulty. We present an evaluation framework that separates what frozen representations contain, how they organize appearance and physical differences, and what changes a model's own prediction error. On IntPhys2, a benchmark of physically possible and impossible events, we compare representations from latent prediction, masked pixel reconstruction, and simple visual statistics. Appearance remains easy to decode, while V-JEPA2 exposes modest information about whether events are possible or impossible. Looking at the latent geometry, appearance changes become smaller compared with differences between videos, their directions line up more consistently across scenes, and their overlap with physical changes decreases in deeper layers. Across action-conditioned models, incorrect actions raise prediction error, while appearance changes also produce substantial responses. In Physion++ video clips, repeating a single frame can produce higher error than the original clip, while changing color throughout the clip can lower it. Using Kubric, a simulation and rendering framework, we find that impossible events can produce lower error than possible events. A fixed error threshold also incorrectly flags many possible events as impossible. A model can therefore represent physical information and respond to incorrect actions without its native prediction error reliably measuring physical surprise.
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.