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
cs.LG
We develop an uncertainty-aware physics-informed surrogate for a one-dimensional - junction diode, conditioned on device length, doping and bias. Using the internal state of the device as predicted by the surrogate we develop a test-suite of quantities of interest including the terminal current, depletion width, peak field and stored charge. The formalism and the quantities are can be extended to asymmetric junction and two-dimensional diodes as shown by means of benchmark analysis. For the one-dimensional symmetric junction surrogate, we obtain 0.11% median error on the electrostatic potential, and 1.5% and 0.61% on the electron and hole densities. Finally, we develop an uncertainty analysis which determines the validity of surrogate answer within the user-specified tolerance.
math.DS
For a time-homogeneous Markov process, the fixed-lag solution operator \( (T_τf)(x)=\mathbb E[f(X_{t+τ})\mid X_t=x] \) of the Kolmogorov backward equation evolves observables linearly and deterministically, even when the dynamics are stochastic. We approximate this operator using a two-stage method where we first approximate this operator directly from data, without knowledge of the governing equation (e.g., Fourier Neural Operator), and then compress the Galerkin projection onto a finite-dimensional observable space that is fixed in advance or selected variationally. The error analysis traces the learning error of the estimator, the sampling error of the Galerkin inner products, and the invariance and reconstruction properties of the observable space to the computed spectra and forecasts. The sampling error enters only through a multiplicative factor. Near an isolated spectral cluster, the invariance defect of a subspace controls its distance from the target invariant subspace. The forecast error is controlled by the one-step error of the reduced model and the projection error of the observable; when the measure is invariant and the reduced model preserves constants and is stable on mean-zero observables, the bound is uniform in the horizon. For deterministic dynamics, a learning rate for Fourier neural operators (FNOs) gives one explicit bound for the learning error. Numerical experiments illustrate spectral approximation and forecasting, including long-rollout stability and a comparison with extended dynamic mode decomposition (EDMD) when fewer transition pairs than basis functions are observed.
cs.AI
Sparse-view computed tomography (CT) reduces the number of acquired projections, but conventional sampling strategies are designed primarily for image reconstruction rather than for downstream physical inference. Here, we investigate optimal task-aware projection selection for directly predicting hemodynamics from sparse CT angiography (CTA) measurements. Using computational fluid dynamics simulations of intracranial aneurysms, we generate synthetic fan-beam CTA projections and train a Fourier neural operator (FNO) to predict two targets: the spatially resolved time-averaged wall shear stress (TAWSS) field and the spatially averaged TAWSS. The FNO was coupled with optimal input selection for simultaneous optimal sampling and training. Our goal was to investigate if agentic AI could discover optimal sampling strategies that outperform current methods. We compared fixed uniform and golden-angle sampling with three task-aware optimal selection strategies: Gumbel-Softmax, a Soft top-K method, and an agentic AI selector. The methods were compared at different view selection budgets. A detailed analysis of the AI agent was performed to understand its reasoning and performance. For spatially resolved TAWSS, Agentic and Soft top-K achieve the lowest mean errors (Agentic performs slightly better) and substantially outperform fixed sampling under extreme sparsity. For spatially averaged TAWSS, optimized selection becomes important at extremely sparse acquisitions. Analysis of the selected masks reveals multiple distinct subsets concentrated around informative regions. Moreover, masks optimized for hemodynamic prediction yield poor image reconstructions, showing that task-optimal acquisition differs fundamentally from reconstruction-optimal acquisition. This work suggests the possibility of designing sparse acquisitions directly around downstream physical quantities.
cs.LG
Physics-informed machine learning (PIML) and hybrid modeling have attracted significant attention as approaches for combining physical knowledge with the flexibility of deep learning. In this work, we investigate whether these approaches deliver their commonly claimed benefits for large-scale photovoltaic (PV) power forecasting. We develop two hybrid forecasting architectures that integrate the ADR physical PV efficiency model with the TSMixer neural forecasting architecture through feature augmentation and residual learning. The proposed models are evaluated on a dataset comprising over 3 million samples from 3,713 PV installations across 33 European countries. We assess convergence speed, forecasting accuracy, transferability across geographical regions, and data efficiency. Although the physics-informed models seem to exhibit slightly faster convergence during training, they do not achieve consistent improvements in test-set accuracy, generalization, or performance under limited training data compared to the purely data-driven baseline. These findings suggest that, for modern deep forecasting architectures trained on large datasets, explicitly incorporating the ADR physical model provides limited practical benefit for day-ahead PV forecasting.
physics.flu-dyn
We investigate the influence of non-dimensionalization on the trainability and accuracy of physics-informed neural networks (PINNs) for buoyancy-driven flows. Using a differentially heated square cavity at and –, we compare thermal-diffusive and free-fall velocity scalings under identical training conditions. The free-fall scaling, with a unit buoyancy coefficient, achieves errors below 1.1% in the mean Nusselt number for , whereas the diffusive scaling, with a buoyancy coefficient of , produces errors of 157–650% and diverges at . We identify a coefficient-induced gradient imbalance, with the dominant buoyancy-related contribution to the loss gradient scaling as , and confirm it through direct gradient measurements. Neither sparse-data supervision nor adaptive loss weighting resolves the training difficulties under the tested conditions. For unsteady convection, the free-fall PINN accurately predicts long-time heat transfer but fails to capture the transient Nusselt-number overshoot. These findings establish non-dimensionalization as an important design consideration for improving PINN trainability in buoyancy-driven flows.
astro-ph.IM
As spectroscopic surveys grow, estimating galaxy properties such as metallicity, star formation rate, and redshift becomes computationally cumbersome. Methods of estimating such properties rely on template spectra or curated redshift catalogs, which fail to represent the diversity of objects seen in large-scale surveys. We present UnEZ, a fully unsupervised, physics-informed machine learning model that can predict spectroscopic redshifts and line strengths with no prior redshift or line strength labels. An encoder predicts emission and absorption line amplitudes/widths, and a fixed deterministic decoder constructs a unique template, estimated redshift, redshift confidence curve, and spectral model. UnEZ was tested on the Sloan Digital Sky Survey (SDSS) Data Release 18 due to its large dataset and thoroughly vetted redshift catalog which serves as an independent benchmark. Despite the lack of templates, line strength labels, or redshift labels, UnEZ's performance competes with modern redshift estimation algorithms. At SNR > 10, UnEZ achieves an outlier fraction of 0.459% and a normalized median absolute deviation (NMAD) of . At SNR > 3, UnEZ achieves an outlier fraction of 3.89% and an NMAD of . Furthermore, we demonstrate how UnEZ's line strength and redshift predictions can be utilized for various purposes such as constructing template spectra required in traditional redshift estimation algorithms. UnEZ illustrates how a fully unsupervised neural network can allow redshift, among other galaxy properties, to emerge naturally from the spectra themselves, providing a template-free, label-free approach that scales to the demands of future surveys.
physics.flu-dyn
Deep lid-driven cavities contain strong motion beneath the lid and much weaker recirculation at depth, so agreement in bulk velocity is an incomplete assessment of a computed flow. We examine data-free physics-informed neural networks (PINNs) for steady, two-dimensional incompressible flow in a cavity of depth-to-width ratio five at Reynolds numbers 100, 250, 500 and 1000. An established hard-constrained streamfunction formulation is combined with prescribed regional collocation, transferred initialization, and selected residual-scaling and envelope variants. Independent spectral/ calculations with the same Gaussian-regularized lid provide the reference fields. For a cavity of depth-to-width ratio at Reynolds numbers , 250, 500, and 1000, evaluation on a common grid gives interior relative velocity discrepancies of 5.130%–7.850%. Over the same cases, floor-region relative velocity discrepancies remain below 5%, with absolute RMS discrepancies ranging from to , where is the lid-velocity scale. In a separate assessment at $\Rey=1000$, the refined workflow lowers interior velocity discrepancy from 5.624% to 2.658% and gauge-aligned pressure RMS discrepancy from to . The improvements compare accumulated training workflows and do not isolate regional sampling. Configuration rankings depend on both region and observable. These finite-budget comparisons establish where the retained workflows agree with the reference and where rotational-field discrepancies remain substantial.
cs.LG
Physics-informed holomorphic neural networks (PIHNNs) exploit complex-analytic representations to satisfy homogeneous PDEs by construction, but their extension to nonhomogeneous problems is nontrivial. We propose a hybrid physics-informed holomorphic neural network (HPIHNN) framework based on a decomposition of the solution into particular and homogeneous components. The particular component is computed by a spectral method on a simple extended domain, while the homogeneous component is approximated by a PIHNN trained only on the boundary with modified boundary data. The resulting formulation avoids meshing complex geometries and retains the dimensionality-reduction advantage of holomorphic representations. The method is applied to nonhomogeneous Poisson, Stokes, biharmonic, linear elasticity, and Helmholtz equations. Numerical experiments covering complex geometries, corner singularities, and nearly incompressible regimes demonstrate that the proposed method accurately resolves the corresponding solutions and, in the considered tests, generally achieves lower errors and shorter training times than standard PINNs. The results indicate that coupling spectral particular solutions with holomorphic neural approximations provides an efficient approach to nonhomogeneous PDEs on complex domains.
cs.LG
Unlearnable data methods (ULD) protect public data from unauthorized model training by adding imperceptible perturbations that create a learning shortcut. A deep neural network can exploit the shortcut learning path to minimize training loss without learning generalizable features. Intuitively, finding adversarial versions of perturbed images that can substantially increase the model's loss can force the model to learn generalizable features. Existing data augmentation based attacks rely on heuristic search strategies/random sampling over a curated augmentation set to identify adversarial augmentation operations, an approach that often does not scale when the number of candidate operations is large. To address the challenge of a large search space, we propose {\techname}, a gradient based adversarial augmentation framework that learns an augmentation policy via stochastic gradient ascent. {\techname} leverages a differentiable data augmentation pipeline to efficiently search a set of up to 18 augmentation techniques, from which a grid search selects a protection-specific subset. The augmentation subset is trained to maximize a surrogate model's classification loss. We introduce a perceptual-plus-pixel regularization to learn operation parameters that preserve image semantics. Under a controlled ablation, {\techname} consistently outperforms an equivalent random sampling baseline (80.0% vs. 77.29% clean test accuracy on EMIN-protected CIFAR-10 for ResNet-18 and 83.28% vs. 66.45% on NTGA-protected CIFAR-10 for MobileNet-V2), demonstrating that gradient guidance drives the clean test accuracy recoverability rather than the expanded search space. {\techname} offers an effective and scalable adversarial augmentation framework for stress-testing ULD methods, a critical tool for developing robust ULD methods.
stat.ML
Deep Gaussian processes (DGPs) are flexible surrogate models for computer experiments with nonstationary response surfaces, but inference over their latent representations remains computationally challenging. Existing methods typically rely on variational inference or Markov chain Monte Carlo (MCMC), which impose variational-family assumptions or require costly posterior sampling. We propose the latent maximum-a-posteriori deep Gaussian process (LaMP-DGP), which uses gradient-based optimization to obtain MAP estimates of the latent representations and enables efficient probabilistic prediction through linked-GP calculations. To scale LaMP-DGP to large datasets, we develop a mini-batch optimization algorithm and, under a polynomial mini-batch bias-decay condition, establish a stationarity bound for latent-state optimization that motivates a growing batch-size schedule. Across numerical experiments and real-data analyses, LaMP-DGP provides consistently competitive predictive performance relative to doubly stochastic variational inference, stochastic gradient Hamiltonian Monte Carlo, and fully Bayesian Vecchia DGP inference. Computationally, LaMP-DGP is substantially faster than the Vecchia MCMC approach while remaining broadly competitive with the stochastic-gradient alternatives. These results position LaMP-DGP as a competitive and computationally efficient alternative for DGP inference. An R package, "LaMPDGP", is available for implementing the proposed method.
cs.LG
Full-order surrogates for high-dimensional nonlinear flows are often unnecessary when applications require only selected degrees of freedom. We propose reduced-order models that bypass full-state reconstruction by deploying graph neural networks (GNNs) directly on coarse meshes. Applied to parameterized 2D/3D confined cylinder flows and an unevenly heated cavity over Reynolds/Rayleigh-number ranges, the models generalize to unseen conditions and accurately predict sparse probe locations and integrated quantities. Coarse-mesh GNNs match or outperform finer-mesh surrogates while reducing training time and memory, even for 3D chaotic dynamics. A dynamics-informed adaptive sampling strategy guided by frequency-spectrum variations reduces maximum errors by an order of magnitude versus uniform sampling at negligible cost. Coarse-mesh training also makes noise-augmented multi-step unrolling practical, improving long-horizon autoregressive predictions. The approach outperforms parametric DMD, sparse MLPs, U-Nets, and Fourier neural operators at lower cost, and enables system identification and state estimation from sparse observations. These results show that coarse-mesh representations, adaptive sampling, and noise-augmented unrolled training form an efficient framework for reduced-order modeling of parameterized unsteady flows without solver-resolution reconstruction.
cs.LG
Machine learning (ML) architectures are being developed for fast emulation of numerical simulators to accelerate both scientific discovery and engineering design. While these approaches are well-tested on popular PDE (partial differential equation) benchmarks, it is necessary to evaluate their performance on datasets that more accurately reflect industrial and engineering applications. We evaluate several computer vision-based architectures trained as surrogate models on a challenging computational physics task involving multiple materials, revealing significant implementation challenges for adapting certain pre-trained models, including transformer-based architectures. For such multi-physics multi-material datasets, our results underscore the importance of learning algorithms designed for sparse and imbalanced data, techniques for adapting spatial encodings and physical consistency metrics, in addition to methods for reducing the cost of generating sufficient training data.
cs.LG
Stellarators offer a promising magnetic confinement approach for achieving controlled nuclear fusion. However, stellarator design remains challenging, as evaluating configuration performance requires computationally expensive, high-fidelity simulations. In particular, key performance metrics derived from guiding center simulations are costly to include directly in the design optimization loop, and are almost exclusively used as diagnostics. Machine learning has the potential to advance fusion research by enabling rapid generation and evaluation of new stellarator configurations. Effectively applying ML for fusion demands large-scale datasets that capture both design diversity and high-fidelity simulation outputs. In this work, we introduce the Benchmark of Stellarator Simulations (BoSS), a dataset of stellarator designs paired with guiding center simulation results and trajectories. The BoSS is the first large-scale dataset of guiding center simulations, containing simulation data for 180,000 distinct magnetohydrodynamic equilibria spanning a wide range of magnetic geometries and confinement properties. To exemplify the utility of ML to accelerate stellarator design, we formulate and address two sets of modeling tasks: generative modeling for designing stellarators with good particle confinement, and surrogate modeling for predicting stellarator heat deposition patterns and particle trajectories. The tasks reveal the potential impact ML can have in the stellarator field and important opportunities to improve the applicability of ML models in the sciences. Our baselines generate diverse, performant stellarators and provide useful surrogate predictions, and point to long-horizon trajectory forecasting and out-of-distribution generation as key directions for future work. The BoSS can be accessed through https://boss.flatironinstitute.org/.
math.NA
Parametric PDEs in science and engineering are often posed on irregular meshes with geometries that may contain holes or complex boundaries, yet popular operator-surrogate architectures such as the Fourier Neural Operator (FNO) rely on structured geometries for fast computational kernels. We introduce Adaptive Modal Operator Refinement (AMOR), which replaces FNO's Fourier-based spectral convolutions with reduced-basis blocks and supports both data-driven and prescribed input/output bases through a common encode/decode interface. AMOR thus applies unmodified to arbitrary meshes and, because its spectral parameterization has no tensor-product dependence on the spatial dimension, it scales favorably to three dimensions, where FNO's spectral weights grow as with the number of spectral modes . We prove that AMOR is a universal approximator of continuous operators. On two-dimensional structured-grid benchmarks, AMOR is competitive with FNO overall and surpasses PCANet: it outperforms FNO on nonlinear diffusion and Helmholtz problems, while a static snapshot basis keeps it from matching FNO's accuracy on the time-dependent Kolmogorov flow problem. On three-dimensional problems it matches or exceeds FNO's accuracy at lower inference cost on linear elastostatics while trailing FNO on a turbulent lid-driven-cavity flow and scales favorably to problems demanding high capacity. On irregular meshes, where FNO is not directly applicable, AMOR reduces the relative error over the FNO extension Geo-FNO by (airfoil) and (elasticity). Finally, AMOR maintains strong performance across three physically distinct, experimentally motivated loading regimes on a topologically nontrivial three-dimensional aircraft-rib mesh, demonstrating its applicability to realistic engineering problems without modification.
cs.LG
We present a survey of approaches to Bayesian inference with simulator forward models, focusing on settings with prohibitively expensive simulators. In this domain, Bayesian optimization-based methods have emerged as the most promising approach. We unify existing methods into a general framework, enabling consistent reasoning about shared algorithmic structure across the fragmented literature. Within this framework, we identify the primary design choices and perform a systematic empirical comparison of their effects on inference efficiency in terms of required simulation budget. A key result of our study is that inference efficiency is often dominated by the choice of surrogate-model response variable, as it directly governs the complexity of the modeled function. Specifically, we demonstrate that the prevalent scalar log-likelihood is a poor response variable, as it discards crucial information. Based on this insight, we introduce the concept of custom \emph{proxy variables}: transformations of simulator outputs engineered to retain more information and provide smoother response surfaces, substantially improving inference efficiency over standard response variables. We provide actionable guidance and a numerically robust Julia package to facilitate practical adoption of Bayesian optimization for simulator inverse problems.
cs.NI
Coordinated spatial reuse (Co-SR) in IEEE 802.11bn increases area throughput through simultaneous transmissions, yet the combinatorial configuration space makes real-time optimization challenging. We propose a sample-and-score approach: draw random Co-SR configurations, score each with a surrogate model, and select the best. The surrogate is trained offline and deployed without online fine-tuning or sequential exploration, yet performs close to multi-armed bandit and heuristic baselines that need multiple interaction steps or extensive measurements. On unseen topologies with 2-16 access points, it recovers 52-77% of a perfect surrogate's throughput. A perfect sample-and-score approach reaches 95% of the upper bound throughput with 8192 candidates.
physics.flu-dyn
The standing wave problem concerns the space-time periodic motion at the free surface of a two-dimensional, infinitely deep, irrotational flow of an incompressible inviscid fluid under gravity. Although spectrally accurate computations have revealed a rich array of nonlinear wave phenomena, repeatedly evaluating their evolution over large parameter spaces remains challenging, particularly when resolving fine-scale spatial oscillations. We employ a Fourier neural operator (FNO) architecture to learn the solution operator along a numerically computed one-parameter family of symmetric standing waves. Given a wave profile at an instant of rest and a normalized observation time, the learned operator predicts the fluid surface, the velocity potential and the dipole density at the surface at that time. In-distribution tests yield uniformly small relative errors within the training range. Two out-of-distribution experiments characterize extrapolation toward contrasting physical regimes. Toward the free-fall limit, errors concentrate near the sharpening crest, consistent with the spectral truncation in the FNO architecture. Toward the linear limit, absolute errors remain small whereas relative errors increase as the amplitude vanishes. A residual of the governing equations, evaluated independently of reference solutions, complements these tests and provides a diagnostic for exploratory predictions beyond the available data.
cs.LG
Wind farm layout optimization becomes increasingly difficult as turbine count grows, especially when high-fidelity aerodynamic models are used. Conventional Kriging-based Bayesian optimization often suffers from low sample efficiency in high-dimensional layout spaces because sparse training data provide limited domain coverage. We develop a Graph-informed Kriging framework that embeds reusable aerodynamic interaction information into the surrogate mean function. The wind farm is represented as a directed aerodynamic graph, where pairwise turbine interactions defined in a low-dimensional relative-coordinate space are assembled into a farm-scale mean. This structured mean captures the dominant variation in annual energy production (AEP), allowing the Gaussian process to model only the residual structure and uncertainty. Numerical experiments show that Graph-informed Kriging consistently improves AEP prediction accuracy over ordinary and generic-trend Kriging under sparse-data conditions, with increasing benefits as layout dimension and wake-interaction strength grow. Embedded in Bayesian optimization, it substantially improves sample efficiency and achieves competitive solutions for the IEA Wind Task 37 benchmark with about 280 AEP evaluations. In a controlled 16-turbine case, it also outperforms ordinary and multi-fidelity Kriging under the same high-fidelity evaluation budget. The framework is further extended to a 48-turbine wind farm, demonstrating applicability to large-scale CFD-based layout optimization. These results show that Graph-informed surrogate modeling can enable more efficient use of high-fidelity aerodynamic models for reliable large-scale wind farm layout design.
physics.comp-ph
Algorithm design tailored to graphics processing units (GPUs) can substantially improve the efficiency of computational fluid dynamics (CFD) simulations. Efforts to adapt CFD solvers to GPUs often focus on spatial discretization, while time advancement commonly relies on multistage Runge–Kutta (RK) methods. However, these RK methods require repeated residual evaluations and full-domain operations, increasing the cost of compressible-flow direct numerical simulation (DNS). To reduce this overhead, we develop a local arbitrary high-order derivatives (ADER) finite-difference method that couples a compact ten-point quadratic predictor to a conservative central corrector through operator matching. With two quadrature nodes, one Picard correction, and selective dissipation, smooth convective tests recover third-order convergence under fixed-CFL refinement and near-seventh-order spatial behavior when background spatial error dominates. Temporal states remain kernel-local, and halo communication overlaps interior computation. Tests of smooth advection, periodic turbulence, and wall-bounded flows assess accuracy and flow statistics. On a -node viscous Taylor–Green benchmark without heat conduction, throughput reaches 230.87 million node updates per second on one V100 GPU in double precision, 1.944 times that of spatially matched three-stage Runge–Kutta integration. Weak-scaling efficiency reaches 99.44% from 4 to 32 V100 GPUs at 1.812 billion nodes.
cs.LG
Generative machine learning provides an end-to-end framework for aerodynamic design optimization by generating diverse aerodynamic configurations conditioned on target performance. However, the generated designs may violate geometric constraints or deviate from the prescribed aerodynamic performance. Therefore, we propose a Condition-Enhanced Generative Adversarial Network (CEGAN) that embeds geometric and aerodynamic information into the generative process. A condition-informed loss function is developed by combining a geometry-guided feasibility penalty with an aerodynamic performance penalty evaluated by surrogate models trained on the same dataset. Additionally, an output filtering mechanism discards infeasible designs using these surrogate models, ensuring compliance with prescribed conditions. The method is demonstrated on aircraft configurations similar to the Cessna Citation X. Each configuration is represented by 28 shape parameters, whose aerodynamic performance is evaluated using OpenVSP. Interpolation and extrapolation tests are conducted for different network architectures and conditioning strategies. Compared with the baseline model, CEGAN reduces the average generation error by at least 36% for interpolated conditions and by at least 46% under extreme extrapolation conditions, while successfully producing diverse and physically feasible designs that extend beyond the training distribution. Therefore, the proposed CEGAN framework offers a robust and accurate tool for rapid aerodynamic configuration exploration during the conceptual design phase.