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
The differential neural tangent kernel (DNTK) is a tool for analyzing the training dynamics of overparameterized physics informed neural networks. In this work, we investigate the symmetry of the infinite DNTK under an orthogonal group, for two layer and deep neural networks separately, based on the explicit expression of the DNTK and recursive formula, respectively. The results are for all activations with or without a bias term, and shed insight into the structure of the infinite width DNTK. Then we prove that the integral operators over the unit sphere induced by operators from the same group orbit share the spectrum, and their reproducing kernel Hilbert spaces differ only by an orthogonal transformation, and that the operator fixed DNTK exhibits zonal symmetry on the unit sphere for symmetric operators. Thus the eigenvalue decay rate of the associated integral operator can be derived for shallow networks with RePU activation and zero bias initialization.
cond-mat.mtrl-sci
Structured scientific spectra encode rich physical information while obeying hard constraints, such as conservation laws and characteristic spectral geometry. Accurate prediction of these spectra is central to materials discovery, yet existing methods often treat them as unconstrained sequences and therefore fail to enforce the underlying physical structure. Taking electronic density of states (eDOS) as the prototypical example, we introduce DeepSciReasoner, a general paradigm for predicting scientific spectra under physical constraints. The framework combines structure-aware spectrum decoding with constraint-preserving physical reasoning, allowing predictions to capture rich spectral structure while respecting the underlying physics. We evaluate DeepSciReasoner on eDOS, phonon density of states (phDOS), X-ray absorption near-edge structure (XANES), and Raman spectra, where it substantially improves prediction accuracy while maintaining physical consistency. These results establish DeepSciReasoner as a reusable blueprint for structured scientific spectrum prediction under hard physical constraints.
cs.LG
The Well, a 15-terabyte dataset spanning 16 physical simulation domains, provides an extensive benchmark for developing and evaluating machine learning surrogate models for complex physical systems. The baselines released with the benchmark were presented by their authors as illustrative examples obtained at small computational cost, trained with zero to very limited hyperparameter tuning and under a highly constraining 12-hour per-run wall-clock limit. These results have subsequently been treated as fully tuned benchmarks, and in some cases effectively interpreted as unconstrained performance baselines. We perform a short non-exhaustive hyperparameter search for the Tucker-factorized Fourier Neural Operator (TFNO) under the same 12-hour per-run wall-clock limit, while using only a single input timestep rather than the history of up to four used by the published baselines. Despite this more restrictive setup, tuning alone reduces VRMSE below both published FNO and TFNO baselines on 15 of 17 tasks, sometimes by several orders of magnitude. This sensitivity to a modest tuning effort underscores that the released neural operator baselines should not be treated as architectural benchmarks.
cs.AI
Earth-system models simplify atmospheric chemistry into condensed mechanisms, because near-explicit mechanisms such as the Master Chemical Mechanism (MCM) are too costly to solve in every grid cell. Neural emulators could lift this limit, but most advance the chemistry in small time steps and cover only a few species or a reduced mechanism. Here we introduce FNO-MoE, a Fourier neural operator with a mixture of experts that predicts the full near-explicit chemical state over 30 minutes in a single call. The same network also guides its own training, using the disagreement among its experts to select the most informative box-model simulations. At equal cost, this active sampling yields a more accurate emulator than random or evenly spread sampling. Fine-tuning on longer trajectories keeps it stable over multi-hour runs in which models trained on short simulations diverge. The resulting emulator reproduces the evolution of thousands of species with high fidelity, remains accurate for unseen chemical compositions and runs orders of magnitude faster than the numerical solver. These results open a new direction for emulating complex atmospheric systems: neural operators that predict the full chemical state over long windows and choose their own training data. Training under changing meteorology is the next step towards bringing near-explicit chemistry into Earth-system models.
cs.LG
Radiative heat transfer plays a dominant role in fire simulations, where solving the radiative transfer equation (RTE) is a computational bottleneck. Neural operators can accelerate these computations by learning solution operators from offline simulation data. However, conventional DeepONet surrogates rely on fixed-grid inputs and affine reconstruction, limiting their flexibility across resolutions and their approximation accuracy at a fixed latent dimension. In this paper, we develop a transformer-based DeepONet for multi-resolution RTE surrogate modelling. The proposed approach combines a Perceiver encoder, which maps temperature and absorption coefficient fields at different spatial resolutions into a fixed-size latent representation, with a cross-attention decoder that enables non-affine reconstruction of the radiative intensity. This architecture allows a single model to process inputs at varying resolutions without resampling them onto a common grid. We formulate a computable empirical version of a previously derived theoretical lower bound for affine reconstruction, enabling direct comparison with model errors on the same dataset. Experiments on a two-dimensional pool-fire dataset demonstrate that the proposed approach outperforms autoencoder-based DeepONets in predicting both radiative intensity and incident radiation, with fewer trainable parameters. Power spectral density analysis shows improved preservation of small-scale structures. Both affine baselines remain above the corresponding lower bound at all evaluated ranks, whereas the proposed model achieves a training error below it at one matched latent dimension, demonstrating the potential of non-affine reconstruction to overcome this representational limitation. Experiments on a dataset combining three spatial resolutions confirm the accuracy advantage of the approach at each input resolution.
cs.LG
The mass concentration of particles smaller than 2.5um (PM2.5) is cheap to measure and widely monitored, whereas the particle number size distribution (PSD) requires costly instruments and is measured at only a few research stations. Yet many aerosol effects, such as vapor uptake, cloud droplet formation and deposition in the human respiratory tract, depend on the PSD rather than on mass. We explore whether recent generative deep learning models can nowcast the PSD: from the PM2.5 record and eight meteorological parameters over a 24h window, a model generates an ensemble of plausible hourly size distributions for the same window, reflecting that one mass can arise from many size distributions. Rather than proposing a single best model, we use two contrasting Finnish stations, the boreal forest site Hyytiälä and the urban site Kumpula, as a controlled testbed. On it, we benchmark six generative models against deterministic and climatological baselines, locally and after transfer between sites, and test physical constraints for neural network training. Flow matching performs best overall; its guided variant has the lowest continuous ranked probability score (CRPS) at both sites. A constraint based on a reduced aerosol general dynamic equation (GDE) lowers the CRPS by 5.5-11.5% at the training site and reduces errors after transfer between sites. Transfer remains harder than local estimation, identifying training on large multi-station data sets as the next step towards PSD estimates at unmonitored locations. This benchmark establishes physics-informed generative models as a promising route from routine air-quality monitoring to size-resolved aerosol information.
cs.LG
Decisions about heat, frost and flooding are made locally, yet reanalyses and climate models resolve tens of kilometres. Generative downscalers add kilometre-scale detail with uncertainty, but are tied to a grid, costly to sample and lack a tractable likelihood. Here we introduce CD-FFM, a functional flow-matching model that treats the high-resolution field as a continuous random field that one model can query at any location and resolution. Its velocity acts pointwise, so spatial variability comes from a noise prior fitted to the observed spectrum and every observation has an exact likelihood. Downscaling ERA5 to 1 km daily temperature over Fennoscandia, CD-FFM lowers the continuous ranked probability score by 27-31% against regression and 12-18% against a forty-times larger neural operator in each of three test years, and outperforms a CorrDiff-style diffusion model while sampling about fifty times faster. The same model transfers to precipitation and makes large kilometre-scale ensembles affordable.
cs.LG
Computational Fluid Dynamics (CFD) is essential in contemporary engineering design, yet it remains expensive to compute and can take thousands of CPU/GPU hours or more for a single high-fidelity simulation. Recent developments in machine learning for scientific modeling have led to powerful surrogate frameworks that can approximate flow fields and physical quantities by using a fraction of the computational cost. However, most of these methods require largescale homogeneous datasets or simple geometries, exhibiting severe generalization gaps when applied to complex and data-scarce configurations. To address this, we propose the Factorized Geometry Convolutional Neural Operator (FG-ConvNO) for robust geometry-aware propeller pressure prediction under limited training data. We introduce geometryaware encoding, efficient interpolation-based decoding, and auxiliary global quantity supervision. In addition, we incorporate DISCO blocks that use discrete continuous convolutions to make the model discretization agnostic. In our experiments, FG-ConvNO achieves the highest accuracy for both surface pressure and global thrust prediction on a procedurally generated propeller CFD dataset. Geometry-aware encoding and architectural simplification improve stability, while random vertex subsampling enhances robustness. Overall, adding geometric priors to grid-based convolutional operators reduces overfitting on complex propeller geometries and improves generalization in low-data regimes.
cs.LG
Diffusion models have become a dominant approach to structure-based drug design. However, because they are trained primarily to fit reference structures, they often place ligands in physically implausible poses that clash with the protein. We introduce MLIPDiff, an inference-time guidance method that can be applied to pretrained diffusion models for ligand generation. The method uses physics-informed guidance from UMA (Universal Models for Atoms), a machine-learned interatomic potential (MLIP). The guidance combines four weighted energy terms (protein-ligand interaction, ligand strain, steric clash, and pocket anchoring) and uses the original model checkpoint without retraining. On CrossDocked2020, MLIPDiff completely eliminates protein-ligand collisions while preserving the ligand's local geometry, improving bond-length distributions and physical plausibility relative to the base model. Compared to models such as NucleusDiff that are specifically designed to reduce atomic clashes, MLIPDiff achieves clash-free structures without compromising local geometry. It maintains the base model's PoseBusters pass rate and attains the best median Vina Score, Vina Min, and Vina Dock, surpassing both the base model and NucleusDiff, with a median of 59.6% of ligands per pocket binding more strongly than the reference. MLIPDiff thus addresses a limitation of prior methods by generating physically plausible structures with favorable predicted binding affinity using a single frozen model and no additional training.
physics.comp-ph
We develop an uncertainty-aware surrogate modeling approach for coupling an atomistic kinetic Monte Carlo (KMC) surface-chemistry solver with a continuum multi-species fluid dynamics solver across disparate physical length and time scales. The surrogate model predicts boundary mass fluxes for six species and their uncertainties, which the continuum solver monitors to automatically trigger additional KMC simulations when new training data are needed. This enables efficient multiscale coupling and maintains a user-specified level of accuracy. We demonstrate the approach for reactive halide-perovskite vapor deposition, which involves a multi-species vapor jet impinging on a reactive substrate. The KMC solver uses a DFT-calibrated energetics model that we construct as part of this work and provides net deposition and desorption rates for six species. With a conservative uncertainty threshold, the surrogate-coupled approach reproduces cumulative mass fluxes of the directly coupled approach with errors typically within 10-20%, while capturing the non-monotonic dependence of net deposition on species partial pressure. Importantly, the results show that detailed crystal structure need not be explicitly represented to predict quantities exchanged between atomistic and continuum solvers; species-resolved mass fluxes provide a sufficiently low-dimensional representation of the atomistic response. For this accuracy target, the autonomous online-learning approach reduces the number of required atomistic simulations by two to three orders of magnitude relative to direct multiscale coupling.
physics.flu-dyn
Thermal-fluid field distributions underpin the analysis and operation of energy infrastructure, from nuclear-reactor cooling channels to industrial heat exchangers, but resolving these distributions through computational fluid dynamics requires prohibitively large simulation ensembles. Their complex geometries also demand unstructured meshes that are poorly accommodated by generative models developed for regular grids. Here we introduce FlowMesh, a generative framework that combines permutation-invariant mesh encoding with deterministic latent flow matching and an l1 penalty on the learned transport velocity. FlowMesh generates full-field realizations directly on fixed unstructured meshes without auxiliary grid interpolation or a stochastic denoising chain. Across lid-driven-cavity, pressurized-water-reactor subchannel and heat-exchanger datasets, evaluated over six matched training seeds, FlowMesh achieves macro-averaged probability-density-function coverage of 91.7%-97.0%, exceeding an architecture-controlled latent diffusion model by – percentage points. Latent-velocity regularization increases coverage by percentage points for reactor flows and 1.1 points for heat-exchanger flows, while reducing temperature-field Kullback–Leibler divergence by 1.7-2.4-fold. Each full-field realization requires 1.23 \pm 0.15 s, providing a 585–1902-fold wall-clock acceleration over computational fluid dynamics. FlowMesh therefore makes large-scale generative characterization of thermal-fluid states computationally feasible, providing a foundation for data-driven analysis and digital-twin development in fixed-geometry energy systems.
cs.LG
State inference and parameter learning for nonlinear filters is a core computation for scientific machine learning with varied applications in engineering and neuroscience. The unnormalized filtering distribution is governed by the Zakai equation, a stochastic partial differential equation (SPDE) that combines the forward Kolmogorov operator (known as the Fokker-Planck equation) with observed likelihood updates. Although solving these high-dimensional SPDEs is often impossible analytically and intractable numerically, advances in operator learning and physics-informed machine learning have made it feasible. Harnessing these advances, we introduce the Zakai Equation Neural Operator (ZENO), a model that optimizes a neural operator against a Zakai Equation based physics-informed loss to approximate the exact unnormalized filtering distribution for latent stochastic dynamical systems. We use this ZENO-inferred posterior distribution in an expectation-maximization (EM) framework to perform parameter learning and state inference. We demonstrate ZENO's ability to accurately infer the posterior distribution and learn its corresponding SDE parameters in three simulated stochastic dynamical systems (Double-Well bistable system, Van Der Pol (VDP) oscillator, and Lorenz system) and compare its performance against established methods for latent SDE inference and learning. We show that ZENO recovers previously observed limit cycles representing forward and backward locomotion from a whole-brain imaging dataset of immobilized \textit{C. elegans} nematodes. ZENO is a novel approach to the problem of nonlinear filtering and dynamical inference through the lens of partial differential equations and operator theory.
astro-ph.SR
Molecular clouds exhibit complex, multi-scale dynamics driven by the interplay of turbulence, self-gravity, and gas pressure. Modelling these systems with conventional grid-based methods becomes increasingly expensive as spatial resolution and dimensionality increase. Physics-Informed Neural Networks (PINNs) offer a mesh-free alternative by incorporating the governing equations directly into the training objective, but their ability to model realistic turbulent self-gravitating flows remains largely unexplored. We apply PINNs to isothermal molecular clouds initialized with astrophysically motivated turbulent velocity fields, considering subsonic and supersonic evolution in two and three dimensions. We benchmark the predicted density and velocity fields against the finite-volume code Athena++. PINNs accurately recover the global evolution of the flow over multiple free-fall times across turbulent realizations, Mach numbers, and dimensionalities. Their training cost also exhibits weak dependence on spatial resolution, increasing by less than 25% from 128^3 to 1024^3 in our experiments. These results demonstrate that PINNs can model substantially more realistic self-gravitating turbulent flows than previously explored and provide a promising complementary framework for studying these systems.
physics.flu-dyn
Interactions between ultrasound and microbubbles underlie a range of biomedical and industrial applications, yet predicting how the physical parameters of the medium and bubbles govern nonlinear wave propagation remains difficult. This study proposes a parameter estimation framework that combines a Korteweg-de Vries-Burgers (KdVB) equation, describing weakly nonlinear wave propagation in a bubbly liquid, with a physics-informed neural network (PINN). The contributions are threefold. First, the PINN reproduces the reference solution of the governing equation in the forward problem, with a near-zero prediction error at the initial time that confirms the initial condition is enforced exactly as intended. Second, prior to inverse estimation, a sensitivity analysis is introduced that quantifies, at both the coefficient and solution levels, how each of eight physical parameters influences the KdVB equation, allowing the expected difficulty of estimating each parameter to be assessed in advance. Third, based on this assessment, single-parameter inverse estimation is performed for seven of the eight parameters using the PINN. Liquid viscosity, bubble initial radius, liquid density, sound speed, and liquid pressure are estimated with errors of 0.8-2.1%, the polytropic exponent converges only partially, and the surface tension coefficient cannot be estimated at all, consistent with the sensitivity analysis. These results establish a general framework for identifying and estimating the physical parameters governing nonlinear wave propagation in bubbly liquids from observed waveform data.
cs.LG
The drift-diffusion equations are the fundamental building block for the modeling, design, and optimization of modern semiconductor devices. Solutions of the drift-diffusion equations rarely give way to analytical forms, and exhibit strong nonlinearity, with the solutions ranging over several orders of magnitude. These attributes have led to research into numerical solvers, and while many commercial Technology Computer Aided Design (TCAD) packages now exist, they may require long simulation times, exhibit sensitivity to initial guesses, and rely on mesh generation. Further, these solvers are not well suited for inverse problems where the design parameters of a device are retrieved from its desired functional characteristics. To address all these challenges, this work demonstrates the usage of Physics Informed Neural Networks (PINNs) for the solution of the drift-diffusion equations with errors comparable to traditional simulation software using advanced training techniques to solve problems beyond the well-behaved equilibrium regime. For this study, we specifically choose an abrupt PN-junction in both one and two dimensions that features extreme gradients of the carrier concentrations at the Ohmic contacts and an abrupt discontinuity in the doping profile. Using the proposed PINN architecture, we are able to retrieve accurate results for all observables under all bias conditions. Additionally, we apply the PINN solver towards the inverse problem of retrieving doping profiles directly from desired electric field distributions or electrostatic potentials under non-zero applied biases. Our work establishes a powerful PINNs-based approach for semiconductor device modeling with the ability to solve inverse problems under non-equilibrium conditions for microelectronics research and discovery.
physics.ao-ph
Computational Fluid Dynamics (CFD) is increasingly used to resolve wind, heat, and pollution patterns in cities with high fidelity but high computational cost. Thermal effects and vegetation are often neglected despite being important drivers, yet their influence may be masked by variability from other uncertain inputs. This work determines how precisely model parameters and boundary conditions must be known for these effects to govern output uncertainty in the velocity, temperature, and concentration fields of a two-dimensional street canyon. A global Sobol analysis of 24 parameters is made tractable by a surrogate trained on Reynolds-Averaged Navier–Stokes (RANS) simulations, combining principal component analysis (PCA) with multilayer perceptrons (MLPs). Two ventilation regimes assess the variance due to thermal and vegetation parameters as uncertainty in all other inputs is progressively reduced. At typical uncertainty levels, turbulence closure constants and inflow turbulence profiles govern variability in all three fields in both regimes. Under weak ventilation, solar forcing becomes the main source of temperature variability once the remaining uncertainties are halved, and of concentration variance once they are reduced to a quarter (about for the dominant closure constant and for the emission rate). In contrast, vegetation contributes significantly at typical uncertainty levels. Under strong ventilation, however, the canopy never overtakes the closure constants, even when the dominant one is known to . Spatially, both effects peak at road level and along canyon walls, which influence outdoor exposure and indoor infiltration, suggesting that high-resolution exposure studies should account for them.
physics.comp-ph
High-fidelity Reynolds-averaged Navier–Stokes (RANS) simulations remain a standard tool for aerodynamic analysis, yet each solve on an unstructured mesh is computationally expensive, making many-query tasks such as design exploration, optimization, and multi-condition evaluation costly. Neural operators provide mesh-flexible surrogates for mapping geometry and operating conditions to flow fields; however, in many existing architectures, global parameters such as the freestream state and design variables are concatenated with pointwise inputs, leaving their influence on intermediate features implicit. This paper proposes CoPiT, a \textbf{Co}nditional \textbf{P}osition-induced \textbf{T}ransformer that builds on the Position-induced Transformer (PiT) as its geometric backbone and injects a global condition vector through multi-stage feature-wise linear modulation (FiLM), thereby making parametric modulation explicit while preserving geometry-based attention weights. The model is evaluated on two-dimensional AirfRANS airfoil fields, including scarce-data and extrapolation regimes, and on three-dimensional BlendedNet++ blended-wing-body surfaces. On the AirfRANS full-data test set, CoPiT reduces surface and volume losses by approximately 54% and 24% relative to Transolver, respectively, and achieves the lowest overall normalized test MSE among the compared baselines on BlendedNet++. Matched ablations show that FiLM conditioning generally improves upon input concatenation, while the preferred placement is task-dependent. CoPiT thus provides a practical operator-learning surrogate for parametric aerodynamics on unstructured meshes.
physics.flu-dyn
Physics-informed machine learning has become a major direction in predictive modeling of fluid dynamics, combining governing physics with learned representations. Yet prevailing formulations neither guarantee that small PDE-residual losses imply small solution errors nor scale effectively with increasing problem size. Here we present the neural basis method (NBM) as a new approach for Navier–Stokes dynamics. NBM is built on a ``representation-then-projection'' principle: fixed neural bases define the representation space, while projection of the governing equations determines the expansion coefficients. The same bases define common coordinates for the parametric solution manifold, recasting operator learning as a parameter-to-coefficient mapping and enabling scalability by removing explicit spatial dependence. For incompressible flow, NBM yields a velocity-only formulation whose residual provides an a posteriori velocity-error estimate, establishing a certified, data-free training objective for coefficient learning. Theoretical analysis and numerical experiments demonstrate the accuracy, efficiency, generalization, and scalability of NBM, with substantial improvements over baselines.
physics.flu-dyn
Direct Numerical Simulation (DNS) of the deterministic Navier-Stokes (NS) equations is widely used to provide benchmark solutions of turbulent flow, but its accuracy and reliability have not been rigorously inspected from a mathematical viewpoint. Here we prove a spatial symmetry invariance theorem (SSIT) of three-dimensional NS equations whereby an exact solution of deterministic NS equations under periodic boundary conditions maintains the same spatial symmetry as its symmetric initial flow, forever. SSIT provides an absolute benchmark test for computational fluid dynamics (CFD). It is shown herein that traditional DNS of NS turbulence quickly violates SSIT, revealing that the spatiotemporal trajectory of NS turbulence predicted by DNS soon becomes badly polluted by numerical noise. Importantly, it is found that even the statistical results of DNS might be unstable, i.e., exhibit sensitivity dependence on the initial flow conditions. In other words, the loss of spatial symmetry in traditional DNS of NS turbulence is not a physical instability but instead a numerical artifact caused by the chaotic nature of the flow. Using the SSIT, it is straightforward to deduce several key properties of NS turbulence, including `ultra-chaos', the so-called `noise-expansion cascade', `permanent memory of symmetric initial flow conditions', and so on. Note that permanent memory of symmetric initial flow conditions suggests that NS turbulence governed by deterministic NS equations subject to symmetric initial flow should have no `mixing', corresponding to non-ergodicity, although ergodicity is one of the most fundamental assumptions of turbulence theory.
physics.flu-dyn
In a zero-gravity cylindrical container, a meniscus can span a square or equilateral-triangular cross-section only at contact angles at or above the respective Concus-Finn critical angles of 45 degrees and 60 degrees. We study strong-form physics-informed neural networks (PINNs) across these thresholds under fixed collocation and optimization budgets. Classical capillary flux balance yields a lower bound on the combined interior and wall residual loss for arbitrary positive sampling densities. In the tested nonexistence regime, several degrees below the critical angles, independently evaluated network losses are 1.6-1.9 times this bound. A polynomial least-squares comparison supports the same geometric interpretation. The PINNs still return smooth graphs with finite axial extent, even though the prescribed equilibrium problem has no spanning graph solution. Their small interior residuals coexist with wall-flux deficits near corners, where adjoining contact-angle conditions demand more flux than a finite-slope graph can supply. Residuals vary on both sides of the critical angle, while the bound tends uniformly to zero at threshold for fixed wall weight. These results give a geometric scale for interpreting the computed loss and locate the incompatibility that a small interior residual can conceal.