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
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.
cs.LG
Reconstructing three-dimensional (3D) complex ocean acoustic fields from sparse measurements is challenging due to highly oscillatory wave structures and restricted sensing patterns/routes. Learning-based approaches fall into two categories. First, purely data-driven models can learn complex field patterns, but do not explicitly exploit wave physics that may enhance interpretability and reduce training costs. Second, physics-informed methods impose a specified physical equation as a reconstruction constraint, but often require environment-dependent parameters that are difficult to acquire. As a result, practical 3D acoustic field reconstruction that is both physically grounded and robust to uncertain environmental information remains largely unexplored. This work takes an alternative route: instead of solving a fully specified wave equation, it extracts a structured representation from wave physics and learns its components from data. From the Helmholtz equation and normal mode propagation, we derive a structured spatial-angular tensor representation, termed the S/c representation. Under a low-rank specialization, it takes the form of a rank-(L,L,1) block-term tensor decomposition, which connects structured sampling patterns/routes used in ocean sensing to sufficient conditions for field recovery. Building on this tensor representation, we propose TIDAL, a neural reconstructor that uses the S/c representation as an inductive bias for structured decoding and aligns information aggregation with the sampling geometry. The neural learner removes the need for known model parameters required by conventional physics-based recovery methods. Experiments across three structured sampling geometries show that TIDAL achieves the best reconstruction performance and fastest inference among baselines, with benefits from the physics-derived representation under limited data and model capacity.
cs.LG
Physics-informed generative models should produce samples that are both data-aligned and physically valid, yet existing methods are often iterative and too slow for practical use. Achieving this with a one-step flow-map model is difficult because both data-distribution and physics-constraint learning are enforced only indirectly through surrogate objectives, making their joint learning fragile for long-range flow maps. We propose \textbf{Physics-Informed Long-Short Flow Maps with Direct Guidance (LSFM-DG)}, which makes direct target computation feasible by decomposing one-step generation into a long flow map for global evolution and a near-terminal short flow map with computable closed-form solutions and physics potentials. As the short flow map shrinks to zero, it provides both direct distributional and physical targets for learning the long flow map. This yields a unified one-step flow-map model that removes Jensen's gap, improves training stability, and achieves stronger data fidelity and physical consistency without distillation.
cond-mat.mtrl-sci
Conventional process optimization of the Metal-Organic Chemical Vapor Deposition (MOCVD) growth parameters to achieve high-quality thin films relies on iterative, resource-intensive experimental runs. While predictive modeling can circumvent this cost and effort, simulating thin-film growth is constrained by the vastly different length and time scales of the deposition process. While continuum (e.g., Computational Fluid Dynamics (CFD)) and first-principles methods (e.g., Molecular Dynamics (MD)) struggle to balance experimental length/time scales and atomistic accuracy, Kinetic Monte Carlo (KMC) bridges this divide by resolving atomistic events whilst remaining tractable at experimental length and time scales. However, the accuracy of KMC relies on kinetic rate parameters that require costly density functional theory (DFT) calculations. In order to circumvent this, we present a framework that calibrates the rate parameters directly against experimental growth data. A forward KMC growth model is coupled in a closed loop with a Monte Carlo Tree Search (MCTS) optimizer that navigates the high-dimensional parameter space, with the search steered by the degree of rate control of each reaction rate parameter. The approach invokes no material-specific assumptions and hence, any deposition process whose forward kinetics can be reduced to a set of rate-controlled events is amenable to the same treatment. We demonstrate it for the MOCVD of GaAs, where the calibrated model captures the characteristic temperature dependence of the measured growth rate. The framework is also able to recover the three well known kinetic regimes characterized by change in the rate determining step from precursor chemisorption to desorption. As a result, the framework converts routinely measured growth data into a mechanistically interpretable model of the deposition process.
cs.AR
Clock meshes are widely used in high-performance VLSI systems to minimize skew and tolerate On-Chip Variation (OCV) in nanometer technologies. However, analyzing meshes is difficult because reconvergent paths and multi-source drivers prevent static timing analysis (STA) tools from handling mesh loops, making SPICE the industrial standard. SPICE simulations are accurate but slow, so clock-mesh synthesis relies on approximate models that overlook critical effects such as non-linear buffer driving caused by input slew and input skew. We propose a Graph Neural Network (GNN) based surrogate model of the clock mesh with a new graph representation and a new architecture that predicts power while also improving the delay and slew predictions at the sinks and capturing the skew histogram under OCV. Trained on SPICE data and tested on unseen real designs, our model achieves average errors of ~ps in delay, ~ps in slew and ~ps in skew, compared with ~ps, ~ps, and ~ps for our prior model, and ~ps delay and ~ps skew for the approximate method used in current state-of-the-art works. Our model predicts power within of SPICE on average, while delivering - speed-ups over the approximate method under OCV modeling, enabling faster and more accurate clock-mesh design-space exploration. A case study on a real design further shows that our surrogate model finds buffering candidates that, at a balanced tradeoff, improves -percentile skew by , reduces power by , and reduces area by at the cost of a increase in -percentile maximum slew as compared to the state-of-the-art work.
cs.LG
Three-dimensional magnetohydrodynamic (MHD) turbulence, the flow of astrophysical and fusion plasmas, is costly to simulate. We present, to our knowledge, the first learned surrogates of three-dimensional resistive MHD turbulence, and compare three standard backbones in that role: a convolutional UNet, a shifted-window transformer and a Fourier neural operator. They are trained as autoregressive emulators of decaying MHD turbulence at a resolution of and Reynolds numbers of 1000, 3000 and 6000, on 500 simulations per Reynolds number, each with one two-stage procedure, single steps and then short rollouts, and stopped by one rule. Over a window of about one large-eddy turnover time, the UNet and the transformer reach relative velocity errors of 0.018 to 0.053 and keep the current sheets, the enstrophy, the current density and the energy spectra of the simulation; which of the two is the more accurate depends on the Reynolds number, the UNet leading at 3000 and 6000 and the transformer at 1000. Applied with the same backbones and training procedure to two public benchmarks, the models reach the lowest error reported to date on the isotropic turbulence set of FactFormer, 39% below the best published model. On the compressible MHD set of The Well, their rollout errors are a third to a half below those of the best of The Well's baselines. They also match a 1.3 B-parameter pretrained foundation model in its rollout windows, with 20-62 times fewer parameters. The code, the configuration of every model, the evaluation scripts and the data generator with the seed of every simulation will be released upon publication.
math-ph
The Lane-Emden Equation is a class of nonlinear differential equations commonly used to model phenomena in astrophysics and mathematical physics, such as stellar structure and thermal behavior in polytropic gas spheres. This study presents a novel hybrid framework that integrates Physics-Informed Neural Networks (PINNs) with boosting methods to enhance the accuracy and robustness of solutions for Lane-Emden type differential equations. Standard PINNs leverage physical laws encoded within the loss function, but their predictive performance can be constrained by optimization challenges and approximation errors. To address this, we introduce a post-processing boosting stage where the residual errors from the PINN prediction are modeled using some regression algorithms - including LightGBM, Random Forest, XGBoost, and Support Vector Regression (SVR). The outputs from these boosted models are aggregated to generate a corrected, high-fidelity prediction. The proposed methodology is systematically validated through quantitative metrics and comparative analysis against the standard PINN baseline. The results demonstrate that the boosted PINN framework significantly reduces prediction error, and improves generalization, offering a powerful and flexible approach for solving scientific and engineering problems governed by differential equations.
physics.flu-dyn
Physics informed machine learning provides a framework to study and simulate fluid dynamics, potentially at a fraction of the computational cost of traditional numerical methods, with the goal of improving the explainability, accuracy and robustness of purely data driven machine learning methods. In this work, we extend the hard constraint projection (HCP) method developed by Chen et al. [Journal of Computational Physics, 445, 110624, 2021] from a linear partial differential equation (PDE) to a nonlinear PDE: the 1D Burgers' equation. To strictly impose a discrete approximation of the governing equation, the Burgers' equation is first locally discretised (using a finite difference stencil) then decomposed into a constraint matrix and a prediction matrix. Using tools from linear algebra, the constraint matrix is used to construct a projection matrix. A physics informed neural network (PINN) [Raissi et al. Journal of Computational Physics, 378, 686, 2019] is used to predict the velocity, and a final unlearnable layer projects the velocity prediction to the hyperplane of exact solutions to a discretised form of the Burgers' equation. Our initial results indicate that the HCP-PINN initially trains similarly to an equivalent PINN, and as the PINN loss plateaus, the HCP-PINN loss continues to decline. When tested on a previously unseen uniform grid of points covering the domain, the HCP-PINN exhibits higher accuracy, converging to a data error approximately an order of magnitude lower than the comparable PINN. We also observe that the inclusion of the HCP layer results in better observance of the governing PDE. Our findings suggest that the HCP-PINN can be more robust to the selection of physics collocation points, and less dependent on collocation point quantity.
physics.flu-dyn
Detailed chemical kinetic mechanisms are computationally expensive in reacting-flow simulations because of their high dimensionality and numerical stiffness. We develop an end-to-end physics-informed autoencoder neural ordinary differential equation (PI-AE-NODE) framework in which an encoder compresses the thermochemical state into a low-dimensional latent space, a Neural ODE advances it continuously in time, and a decoder reconstructs the temperature and all species mass fractions. Elemental conservation, mass conservation, and enthalpy consistency are embedded in the training objective. The framework is applied to H/air, NH/air, and CH/air autoignition using detailed mechanisms of increasing size and complexity, which are represented accurately with only a few latent variables. Compared with an otherwise identical data-driven model, the physical constraints improve ignition delay prediction and conservation behaviour. The models reproduce major and intermediate species evolution at both training and unseen conditions, and their latent dynamics permit efficient explicit integration, with the computational advantage over the detailed mechanisms increasing with mechanism size.
cs.CE
In multiscale systems, nonlocal interactions among spatially distributed constituents can unlock collective, potentially emergent behavior irreducible to individual constituent responses. Beyond characterization, nonlocality in multiscale systems is increasingly viewed as a design element across fracture mechanics, wave physics, and disordered systems. Existing nonlocality theories provide rigorous descriptions and mechanistic insight, but often require prescribed analytic forms, range, symmetries, or periodicity. Machine learning offers a data-driven route to learn interactions, yet principled approaches that tie the network design to physical theory remain nascent. Here we present domain-decomposition attention neural operator (DANO), which learns configuration-dependent interactions in heterogeneous systems governed by linear field equations from field data alone. Through a case study in large-scale optical metasurfaces, we demonstrate DANO's full-field prediction under geometric heterogeneity and across drive conditions, small-to-large domain transfer, and multifunctional inverse design, with learned interactions validated through physics-based interrogation. As an AI-for-Science tool, it supports interaction discovery and scalable, customizable design of nonlocal multiscale systems, including virtual-reality optics.
stat.ML
Physics-informed Gaussian process (GP) methods provide a probabilistic framework for PDE solving. Existing approaches incorporate PDE information in different ways: pointwise conditioning uses the governing equation only at finitely many selected locations, globally constrained GPs restrict the admissible functions to satisfy the PDE exactly, and residual-penalized methods control the PDE mismatch over the whole domain through an additional penalty weight. What is still missing is a GP formulation that directly incorporates global PDE-residual information of the entire domain into its covariance structure, while retaining model flexibility and standard GP conditioning without a separate residual-weight parameter. To solve this issue, this study proposes PDE-residual-informed Kriging (PRIK) based on a PDE-residual kernel. The PDE-residual kernel is constructed by equipping a kernel-section space with an inner product defined by the inner product of PDE residuals. This construction makes PRIK yield the posterior mean with minimum integrated squared PDE residual. It also provides direct statistical interpretations: the variance-scale estimate equals the normalized PDE-residual energy (i.e., the integrated squared PDE residual of the posterior mean divided by the number of labeled observations), and the profile likelihood balances this residual energy against model complexity. Under the stated regularity and stability conditions, we establish -quasi-optimality and convergence rates for the posterior mean, together with a nonasymptotic bound for its PDE-residual norm. We further show that the normalized posterior kernel converges to a variational Green-type kernel and derive a uniform nonasymptotic contraction bound for the posterior variance. Numerical studies provide empirical evidence consistent with the theory and demonstrate the PDE-solving capability of PRIK.
cs.LG
The bottleneck of attention mechanisms, which are the fundamental building block of modern language models, is their quadratic complexity in terms of context size. There has thus been an increasing interest in the compression of the context, also called KV-cache compression. In this article, we consider the problem of compressing the context of attention mechanisms by first formulating it in the Hilbert space associated with its kernel. In this formalism, attention can be represented as the ratio of two linear maps whose interpolant is also the ratio of interpolants, this allows us to consider the interpolation of the linear maps directly. We thus introduce two novel KV-cache compression methods which we call GAIM and Q-DAIM, based on the Generalized Empirical Interpolation Method (GEIM) and the Q-Discrete Empirical Interpolation Method (Q-DEIM), respectively. As the cost of these methods is quadratic in terms of context length, we propose surrogate models based on the Taylor series, the Performer and the Random Fourier Features method which allow the compression to be done in linear time. Finally, we extend this result to the streaming attention setting, providing new methods which allow one to penalize the selection of interpolation nodes based on the previously interpolated context and to update the previous interpolation based on new information. We then provide numerical results on the convergence of the residuals and the output error in future queries and preliminary results on the LongBench-E benchmark showing performance comparable to the state-of-the-art methods. These experiments suggest that the range revealed by our Q-DAIM method could help identify where information is concentrated in the KV cache, thus enabling an efficient compression.
physics.comp-ph
Classical computational fluid dynamics (CFD) methods encounter significant computational bottlenecks in large systems and at high Reynolds number flows due to the rapid increase in degrees of freedom, even on flagship supercomputers. As quantum computers emerge, the Quantum Lattice Boltzmann Method (QLBM) has been proposed as a quantum-native alternative for solving fluid dynamics problems. However, until recently, nearly all studies have relied on classical quantum simulators rather than real quantum hardware. This study presents a benchmark of a one-dimensional QLBM implementation executed on three different IBM Quantum hardware. We design and test a quantum circuit for the advection-diffusion equation using amplitude encoding, a Bhatnagar-Gross-Krook (BGK)-type collision operator, and a streaming step with periodic boundary conditions. Our numerical experiments evaluate transpiled two-qubit gate count, total circuit depth, runtime, and accuracy metrics including maximum absolute error ( norm) and root-mean-square error (RMSE). We find that the present collision and streaming operators dominate the overall cost and become the primary scalability bottleneck on current hardware. To mitigate the prohibitive cost of full quantum state tomography on hardware-based benchmarking exercises, we introduce a sampler-based measurement strategy that reconstructs macroscopic density fields directly from computational-basis measurements. This approach substantially reduces measurement overhead while preserving the expected advection-diffusion dynamics on hardware. These results provide a quantitative assessment of QLBM performance in the noisy intermediate-scale quantum (NISQ) regime and identify the principal algorithmic and experimental limitations that must be addressed for QLBM to become viable for fluid dynamics.
math.NA
We introduce NEOPIC, a framework for learning the field operator in particle-based methods applied to kinetic plasma simulations. Its key novelty is a neural operator that acts directly on the empirical measure of the particles, rather than on a grid, and is evaluated at the particle positions. No mesh or tree is needed and, unlike grid-based neural operators, no deposition onto a mesh takes place, so the particle noise that dominates the inputs of particle simulations is not aliased. Since it replaces only the field solve, it serves as a plug-and-play field solver for particle-based methods: it can be trained on data from particle-in-cell, particle-in-Fourier or tree codes, and combined with any time integrator, including implicit schemes. We prove that the discrete evaluation coincides with the continuous operator at any number of particles (representation equivalence) and derive an error analysis that separates sampling, learning and time-stepping errors: up to the learning error, NEOPIC has the error structure of standard Monte Carlo particle methods. We show that the particle noise in the training data acts as an implicit regularizer, which gives guidance on the number of training particles in relation to the particle numbers used at inference. A complexity analysis shows that NEOPIC is an method whose constants are set by the architecture alone, independently of any mesh or tree. Numerical experiments on electrostatic benchmarks in two and three dimensions, including Landau damping, two-stream and bump-on-tail instabilities, a cyclotron mini-app and a Penning trap, confirm the theoretical findings. A single model trained on several mini-apps generated by different reference methods captures all of them and remains stable up to twice the training time window, which points towards foundation models for fields in particle-based methods.
physics.flu-dyn
This study introduces a new approach for building surrogate models, in the form of Reduced Order Models (ROMs), for PDE-constrained optimization. A physics-constrained data-driven framework is developed to transform large-scale non-linear optimization problems into ROM-constrained optimization problems. Unlike conventional methods, which suffer from instability of the forward sensitivity function, the proposed approach projects optimization problems to system dynamics optimization problems in Hilbert space to increase stability, diminish memory requirements, and lower computational cost. The present approach is applied to shape optimization of a 2D flapping wing section at , where the non-linear interaction of the wing with fluid includes chaotic flow structures. It is shown that the proposed approach can significantly enhance the time-averaged thrust force and propulsive efficiency by 37% and 40%, respectively. We also tested this approach for a 3D flapping wing and the results reveal the potential of the proposed approach for more complex optimal designs in the aerospace industry.
cs.LG
This work develops a physics-informed multimodal deep learning framework for 10- to 110-minute-ahead probabilistic photovoltaic power forecasting. The forecasting model is built on a four-branch architecture that separately encodes plant-level temporal history and inverter-level spatial cloud dynamics through a graph attention encoder with a learned adjacency, known-future solar geometry, and the current meteorological state, fused through gated cross-attention. The geometry branch adds two forward-looking physical signals, spatial cloud heterogeneity and inverter ramp-down activity, each empirically weighted toward the horizon where it is most predictive. The decoder anchors its prediction to a smart persistence baseline, learning a horizon-conditioned correction, and the resulting quantile forecasts are calibrated online through a kernel-weighted adaptive conformal calibration step. The proposed model outperforms all 14 baselines, achieving a forecast skill score (FSS) of 0.2950, 0.099 above the next-best model. A branch-composition ablation shows that every branch contributes positively and the model retains substantial skill in challenging overcast and variable sky conditions (FSS 0.198 and 0.255).
cs.LG
Rapid intensification (RI) is one of the most dangerous and unpredictable phases of tropical cyclones, and its environmental and structural drivers are difficult to identify and separate in observations. Here we introduce CausalVisionRI, a causal-prior-constrained deep-learning system for 24-h RI warning in the western North Pacific. It integrates infrared remote sensing imagery, atmospheric and oceanic fields, and an observationally discovered causal graph into a unified model. The graph and eight sign-verified effects on 24-h intensity change provide an auditable causal prior for training. Discovered from 522 cyclones in 2000-2017, it identifies causal pathways linking atmospheric and oceanic conditions, the cyclone's dynamical and structural state, and its 24-h intensity change. On a forward holdout covering 2020-2024 and 3,004 records, the five-member ensemble achieves a Brier skill score (BSS) of 0.259 relative to a fixed development climatology, significantly exceeding four reference systems; the three LDA baselines reach at most 0.105. It also attains higher detection rates than a published knowledge-block scheme and a reconstructed contrastive-learning scheme at matched false-detection rates under our USA 30-kt standard and the published RITCF standard. Ablations show that the graph pathway adds 0.032 BSS across the holdout and 0.063 over 2020-2021, with a significant contribution in one ensemble member. A deep-learning model constrained by observationally discovered causal structure thus offers a new route to physically informed RI warning.