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.
4,567 papers in Physics-informed · newest first
cond-mat.mtrl-sci
The prediction of response tensors from magnetic textures is a crucial challenge in the study of noncollinear magnets. Existing methods for constructing descriptors of a given response tensor are limited to first-order multipole expansions or restricted to simple magnetic structures. In this work, we construct a complete symmetry-invariant descriptor basis for arbitrary crystal structures and magnetic textures, providing interpretable features for machine learning modeling of response tensors. We modify the standard principal component analysis framework and derive uncorrelated order parameters that are hierarchically stable: extending the order parameter space to include higher-degree spin order introduces additional order parameters that are uncorrelated to the previous ones. We apply this framework to regression and classification of the anomalous Hall conductivity (AHC) in a magnetic kagome lattice. In particular, in the regime where AHC is well modeled by linear regression of the symmetry-invariant order parameters, we find that the squared regression coefficients, ranked by their magnitude, obey a Zipf-like power law: . Our method provides a systematic route to construct interpretable order parameters of all spin orders that connect the symmetry of a magnetic crystal to its response tensors.
cs.LG
Physics-informed neural networks (PINNs) reduce or eliminate the need for large labelled datasets by enforcing governing equations during training. Physics-informed Deep Operator Networks (PI-DeepONets) extend this approach to learning solution operators, enabling rapid prediction across families of problems. Despite these advantages, we show that their application to higher-dimensional problems remains limited by the computational cost of training. To address this issue, we propose a modified PI-DeepONet architecture that reduces this cost by removing redundancy in how the Branch network processes input functions across collocation points. The proposed formulation is mathematically equivalent to the original architecture but reduces input tensor sizes and the number of Branch network evaluations. We analyse the computational complexity of both architectures and derive theoretical scaling laws for training time with respect to the number of collocation points and input functions. The proposed architecture is evaluated on 1D, 2D, and 3D linear advection problems. In all cases, it achieves comparable predictive accuracy to the original PI-DeepONet while consistently reducing training time. In 2D experiments, a maximum speed-up of is observed, with empirical training-time scaling agreeing with the predicted linear dependence on collocation points and input functions. Furthermore, training a 3D model on an NVIDIA A100 GPU is only feasible using the proposed architecture, as the original formulation exceeds memory limits. These results demonstrate that careful consideration of how PI-DeepONets are implemented can yield substantial gains, enhancing the practical performance of PI-DeepONets and enabling their application to otherwise intractable physics-informed learning problems.
cs.CV
Geo-foundation models (GFMs) are typically evaluated by downstream task predictive performance, revealing little about which physical features they are sensitive to or use in prediction. This limits developers' ability to test hypotheses about model behaviour and users' ability to select models for new tasks. We propose Physics-Informed Concept Probing (PiCo), a post-hoc framework for explaining GFM predictions. PiCo identifies concept vectors in a GFM's embedding space by generating synthetic multispectral satellite observations from a 3D radiative transfer model coupled with a game engine. These vectors reveal physical sensitivities that inform domain-based hypotheses about downstream performance. Projecting embeddings onto these concept vectors produces low-dimensional representations for quantifying concept importance in making predictions. We evaluate PiCo on three GFMs with different input modalities using seven physical concepts covering forest leaf optics and canopy structure. In ground-cover estimation, RGB restriction reduces dry-matter sensitivity and disproportionately degrades predictions for dry vegetation and bare ground, supporting a hypothesis derived from sensitivity analysis. For hierarchical forest type and tree species classification, concept representations retain 70.0-93.8% of full-embedding accuracy. Models capture similar physical contrasts between classes, such as structural differences between broadleaf forest and cleared ground and leaf-water-content differences between oak and beech, yet differ in the strength of these contrasts and the concepts driving classification. PiCo thus provides a physical basis for hypothesis testing and model assessment, with potential applicability beyond Earth observation wherever forward models enable controlled simulation and pretrained embeddings are accessible for probing.
cs.LG
A staged physics-informed neural network (PINN) is proposed for identifying the inductance, capacitance and parasitic resistances of a DC buck converter from time-domain data. Gradients are released in the order of L to C to rL to rC, a sequence derived from sensitivity analysis. The five-stage schedule recovers L and C to within 5% and the series ESR to 10%, while a three-stage variant attains the same accuracy 11% faster. An 84 factorial sweep confirms that the trained PINN remains accurate for simultaneous 8% perturbations of all four components, achieving a waveform RMSE of 2.6 x 10-2 over 5 ms-an order-of-magnitude better than a simultaneous-training baseline.
cs.LG
Physics-informed neural networks provide a flexible framework for learning parametric PDE solution families without labeled data, yet preserving accurate derivatives across heterogeneous regimes remains challenging. Structured neural solvers offer compact representations, but restrictive conditional parameterizations can limit adaptation across the solution family. We introduce BeTINN, a structured conditional architecture extending time-induced modulation through multi-directional time-parameter conditioning and a joint residual pathway. We evaluate BeTINN on the Heston stochastic-volatility PDE, a demanding parametric problem with mixed derivatives and economically relevant first- and second-order sensitivities. BeTINN improves joint accuracy across normalized option value and key sensitivity metrics relative to our baselines. Controlled ablations characterize the roles of its architectural components. We further find that validation physics loss is informative but does not fully determine differential fidelity, and that accurate solution values can coexist with localized derivative errors. These results support structured conditional adaptation and motivate derivative-aware evaluation when sensitivities are downstream quantities of interest.
physics.comp-ph
We present a global-in-time spectral Duhamel-Picard method with polynomial expansions for post-exposure bake (PEB) simulation. The coupled acid-quencher reaction-diffusion equations are reformulated as nonlinear Volterra integral equations using the Duhamel principle. Full trajectories are represented by finite polynomial expansions, with temporal coefficient fields determined over the bake interval by Anderson-accelerated Picard iteration, thereby avoiding sequential time marching. In 3-D PEB simulations, we employ Chebyshev and Legendre temporal bases while evaluating the Duhamel integrals using the corresponding Gaussian quadrature rules. We demonstrate that the proposed method simulates a large domain of voxels on the order of one minute. The representation is further incorporated into a physics-informed neural operator (PINO) with a mixed-transform variant of a factorized Fourier neural operator, which is trained without precomputed solution trajectories. Together, the integral formulation and its PINO extension enable accelerated, time-marching-free prediction of concentration fields at arbitrary times within the bake interval.
stat.ML
Compartment models of infectious diseases are often linear in coefficients that are physical parameters or products or ratios of them. We exploit this with closed-form least squares and equip the estimates with distribution-free uncertainty. Physics-informed regression (PIR) fits the parameters to finite-difference derivatives of the data; we introduce physics-informed weak regression (PIWR), which integrates the model in time instead, needs no derivatives of the data, estimates the initial state jointly and is high-order accurate. To quantify uncertainty we wrap both estimators in split conformal prediction, with a calibration population generated by the physics-based model itself, giving simultaneous intervals for all parameters with a finite-sample coverage guarantee. A residual-adaptive factor, computed without ground truth, scales the intervals to each data set (PIWR-RACC). On the eleven benchmark models of disease-informed neural networks (DINNs), PIWR or PIR-FD6 is one to four orders of magnitude more accurate than the reported DINN results wherever the sampling resolves the dynamics, in about a millisecond per fit instead of minutes to hours of training, and the 90% intervals achieve 87-92% coverage in all 88 settings. On the S3I3R model of the original PIR study, PIWR lowers the reported PIR errors by about three orders of magnitude. On real data from the 1978 boarding-school influenza outbreak, a variable-projection variant gives calibrated 95% intervals that overlap those of a Bayesian analysis. On a time-varying transmission benchmark, a B-spline expansion of beta(t) keeps PIR and PIWR linear; they are more accurate than physics-informed neural networks in three of four cases and comparable in the noisiest, with simultaneous bands for beta(t). The complete conformal calibration takes less than two minutes for every benchmark.
cs.CE
Deep learning has enabled substantial advances in oncology, including cancer detection and diagnosis, medical image analysis, tumor characterization, treatment planning, response assessment, and outcome prediction. However, conventional data-driven models often require large annotated datasets, exhibit limited generalization across heterogeneous clinical settings, and lack explicit mechanisms for incorporating the physical, physiological, and biological principles underlying cancer development and treatment. Physics-informed deep learning (PIDL) integrates governing physical laws, mechanistic models, physiological constraints, and domain knowledge into deep learning frameworks, providing a principled approach for learning from sparse, noisy, and heterogeneous oncological data. This review presents a task-oriented synthesis of PIDL methods across oncology, encompassing neural networks, Kolmogorov-Arnold networks, convolutional and vision architectures, neural operators, generative models, and hybrid physics-data-driven frameworks. Their applications are examined across cancer detection and diagnosis, image reconstruction and analysis, tumor characterization, quantitative imaging, tumor progression, treatment response, radiation therapy, treatment planning, and multimodal clinical modeling. Based on the synthesized methodological and application-level evidence, we develop task-optimized PIDL workflows that align the clinical task with appropriate data representations, physical constraints, model architectures, and validation strategies. We further analyze key challenges, including physical-model fidelity, computational scalability, uncertainty quantification, domain generalization, standardized benchmarking, and clinical validation.
cs.LG
Advection-diffusion plays an essential role in transport phenomena such as atmospheric and cloud dynamics. Improved forecasting of cloud motion, in turn, enhances solar power production forecasts and facilitates the integration of additional photovoltaic (PV) sources into the power grid. However, both classical numerical models and emerging deep learning approaches face challenges when applied to spatially irregular sensor networks such as those formed by weather stations. In this work, we adopt a graph signal processing perspective and model advection-diffusion particles as signals on a graph to capture the dynamics of these processes. We introduce a Physics-Informed Graph Neural Network (PING) for forecasting future advection-diffusion particle concentrations on irregular grids. The model incorporates a discretized advection-diffusion equation as a soft constraint in the loss function to guide learning toward physically consistent solutions. This model is on par with state of the art models on synthetic and real transport phenomena datasets, including sea surface temperature and cloud index datasets. Furthermore, the PING model is successfully coupled with models for forecasting PV power production. This hybrid approach leverages data fusion from ground-based sensors at PV stations and satellite images with cloud concentration to improve the accuracy of intra-day PV power production.
cs.LG
Modern Transformers rely on many scale-control mechanisms, including normalization, residual scaling, attention temperatures, loss weighting, and adaptive updates. To explain how these mechanisms maintain scale consistency, we introduce Neural Dimensional Analysis (NDA), a unified framework based on dimensional consistency. We define neural units that specify how tensors rescale and which quantities can be added, just as physical units do in physics. Our rules match residual units, nondimensionalize attention and gate inputs, combine losses across units, and convert gradient units into parameter units. We implement NDA through dimensionless Unit Violation Indices (UVI) for diagnosing scale mismatches within Transformers, a unit-consistent multi-loss objective, and the Gauge-Canonical Transformer (GCT) with normalized coordinates and orthogonalized residual additions. In language-model experiments spanning 51M to 1B parameters, GCT remains stable during training across a broad sixteenfold learning-rate range, outperforming Pre-LN, LLaMA-style, and QK-Norm in 124M validation loss at tuned learning rates. GCT's normalized residual stream also shows improved robustness to quantization. At 1B parameters, calibrated per-tensor int8 quantization increases GCT's validation loss by only 0.009 nats, compared with up to 5.51 nats for the baselines. Vision and physics-informed neural network experiments further confirm NDA's benefits beyond language modeling. These results establish dimensional consistency as a neural network design principle.
physics.flu-dyn
Rarefied nonequilibrium flows are described by the Boltzmann equation, which can be solved using stochastic particle or deterministic methods. With advances in computing, data-assisted physics-informed neural networks have been widely used for flow prediction by combining governing equations with measured or computed data. Data-free PINNs do not require such training data and have been widely studied for continuum flows, but their application to rarefied flows remains limited. This study develops a data-free Fokker-Planck physics-informed neural network (FP-PINN) to describe rarefied nonequilibrium flows. The physics loss is constructed from the ellipsoidal statistical Fokker-Planck (ES-FP) equation using a velocity distribution function (VDF) closure and moment projection. The FP-PINN is evaluated for a steady one-dimensional Mach 10 normal shock. The FP-PINN results agree with the numerical ES-FP results, with errors below . Compared with the particle ES-FP results, the FP-PINN predicts a sharper shock structure with errors up to . This difference is attributed to the VDF closure and moment projection.
cs.LG
Inferring tumor-growth laws from sparse, noisy observations requires more than accurate curve fitting. We study an AI-assisted workflow involving symbolic regression, mathematical admissibility checks, coefficient refitting, and large language model (LLM) ranking. Synthetic Gompertz data allow trajectory fit, forecasting, and recovery of the governing growth law to be assessed separately. A dense noiseless control recovers the generating family, but sparse noisy sampling frequently leads to alternative forms. Among retained candidates in the tested configurations, physics-informed neural network refitting often increases growth-law error, whereas classical nonlinear least squares usually reduces it. A separate exploratory analysis of archived LLM rankings shows no consistent improvement over selection by training error and identifies errors in mathematical reasoning. Plausible saturation, accurate trajectory fits, and convincing explanations can therefore coexist with incorrect growth laws. Mathematical validity and law recovery require evaluation alongside predictive performance.
cs.LG
Accurate long-term air quality forecasting is challenging due to long-range transport, meteorological variability, and nonlinear chemical reactions underlying secondary pollutant formation. Purely data-driven models often suffer from long-horizon drift and lack physical consistency, while existing physics-informed approaches commonly follow open-loop designs that fuse neural and physical components only at the output level. We propose AeroChem, a closed-loop physics-informed state space framework for chemically reactive air quality forecasting. AeroChem adopts a two-branch co-correction design: a UDE-based process branch provides a structured but imperfect physical prior, while a Mamba-based virtual measurement branch captures long-range temporal context and produces probabilistic virtual observations. Neural Kalman Fusion couples the two branches by correcting the latent physical state at each forecasting step and feeding the posterior state back into the simulator, reducing long-horizon drift. We further introduce HanoiAir, a real-world dataset integrating pollutant concentrations, meteorology, and emission inventories. Experiments on HanoiAir and a public benchmark show that AeroChem improves long-horizon stability and sudden-change forecasting.
cs.LG
Physics-informed generative models augment a data-fitting objective with residual penalties that encourage physical constraints to hold in generated samples. However, improving constraint satisfaction need not improve fidelity to the data distribution. We study this conflict in residual-regularized diffusion models and identify two possible consequences. First, the same prediction error can incur different residual costs near different feasible states, preferring states with lower residual sensitivity (avoidance). Second, this preference can extend to feasible states outside the data support, where the residual also vanishes (leakage). Motivated by this analysis, we propose a data-anchored penalty that weights prediction errors by the residual Jacobian at the clean training sample and normalizes the resulting magnitude. This removes the incentive to relocate to less sensitive states without changing the model architecture or sampling procedure. Experiments on a controlled synthetic system, three PDE systems, and molecular transition-state generation with flow matching demonstrate the benefits of anchoring. Code is available at https://github.com/TanjaBien/anchored_diffusion.
eess.SP
In this paper, we consider joint beamforming and power allocation for a mobile multiuser MIMO integrated sensing and communication (ISAC) network with clutter, residual self-interference, and outdated channel state information, under per-user rate and sensing signal-to-interference-plus-noise ratio (SINR) constraints that must hold on every realization. The design must be recomputed every block, and distant or weak targets can make the sensing constraint unmeetable. We propose a physics-informed unsupervised learning (PI-UnSL) network that corrects the analytical design, meets the power and norm constraints exactly by construction, and is conditioned on closed-form interference statistics, spanning the whole tradeoff in one pass. We derive a closed-form sensing SINR at the interference-aware combiner, yielding a necessary range-radar-cross-section-power condition and a priority-independent analytic violation floor, so the problem is intermittently infeasible. We then show that a dual targeting below the attainable floor has no fixed point, and calibrate the label-free objective against the measured floor. Numerical results confirm the floor and the bounded calibrated dual, and show that PI-UnSL substantially raises per-realization joint quality of service over the closed-form baseline, delivers more rate than time-division ISAC at matched detection over most of the tradeoff, and exceeds the reliability of an uncalibrated alternating-optimization solver at a fraction of its latency. More broadly, the physical knowledge given to the network, not its architecture, makes such problems learnable without labels: five architectures fail alike from scratch and perform alike when started from the closed-form design and conditioned on its interference statistics.
math.ST
Data and the governing partial differential equations (PDEs) of continuous-time dynamical systems provide rich structure for statistical learning. A central challenge is how to integrate data with PDE constraints in a principled way to improve generalization. In this paper, we characterize the statistical estimation and generalization properties of learning solutions to the heat equation with a noisy source function from finite, randomly sampled data. We first derive a novel variational formulation, which we characterize as the minimizer of loss function for an energy regularized and ellipticity debiased Sobolev regression. By formulating the learning task as a supervised problem over space-time domains under physically meaningful norms, our approach goes beyond the traditional supervised learning framework by effectively leveraging \emph{auxiliary data}—samples of the source function of the heat equation—to design a \emph{physics-informed energy regularization}. Our analysis reveals that learning in linear parabolic PDEs exhibits intrinsic anisotropy between spatial and temporal regularity, in sharp contrast to the static elliptic problems, leading to fundamentally different estimation and generalization behaviors. Specifically, we derive non-asymptotically rate-optimal estimation errors, as well as generalization error, which explicitly capture the interplay among temporal sampling, spatial resolution, and solution smoothness. Our numerical experiments demonstrate substantial orders of magnitude of reduction in testing errors against various physics-informed neural network methods on various parabolic and hyperbolic PDEs.
stat.ML
We introduce stochastic physics-informed neural networks (SPINNs) for stochastic boundary-value problems (SBVPs) with random operators. The method enforces physics through a structural probabilistic coupling: a common Gaussian stochastic germ drives both the SBVP random operator and a manifold-based stochastic neural architecture. The stochastic neural network is non-feedforward and intrinsically random. A latent Gaussian field and an inhomogeneous Poisson point process on a compact, boundaryless, multiply connected manifold generate random neuron locations, geodesically local sparse connectivity, and a sparse random weight matrix, all governed by a low-dimensional hyperparameter. For deterministic inputs, the network output is random and can represent non-Gaussian random operators. Training is performed in observation space: SBVP simulations produce random observables, while the SNN defines a predictive conditional probability density function. The supervised objective combines data fidelity, through negative log-likelihood, with a cross-entropy alignment term relative to the SBVP-induced conditional distribution. The resulting target is a convex mixture of observation-induced and SBVP-induced distributions, with a dimensionless parameter controlling robustness to model–data mismatch. The shared stochastic germ yields common-random-numbers Monte Carlo estimators and reduced-variance gradients. The method uses only evaluations of the SBVP solution mapping, without differentiating or modifying it, and avoids PDE-residual or boundary-penalty losses. A stochastic elliptic problem on a periodic cylindrical surface illustrates the approach in SBVP-consistent and SBVP-misspecified regimes. A generalized-posterior formulation is also outlined for hyperparameter inference and posterior averaging without per-query reoptimization.
hep-th
Can a holographic theory be reconstructed from its equation of state? We investigate this question using physics-informed neural networks in the bosonic-mass sector of the Pilch–Warner model. We first validate the PINN approach against an analytic solution encoding the leading high-temperature corrections to the conformal equation of state. We then reconstruct nonlinear black-brane geometries and the scalar potential using thermodynamics, ultraviolet asymptotics, Ward identities, and horizon regularity. Independent solutions of the bulk Einstein-scalar equations demonstrate that accurately reproducing thermodynamics with a trained PINN does not guarantee an accurate reconstruction of the scalar potential. High-precision knowledge of the high-temperature equation of state constrains nonlinear interactions in the bulk scalar potential. Fixing the cubic coupling to its exact PW value, motivated by this high-temperature extraction, reduces the maximum sampled error in the reconstructed scalar self-interactions by a factor of compared with constraining only the bulk scalar mass. Adding knowledge of the bulk viscosity of the gauge theory plasma further reduces this error by an additional factor of , with independent forward solutions reproducing the bulk viscosity within .
physics.flu-dyn
Despite widespread enthusiasm, applying artificial intelligence and machine learning (AI/ML) to turbulence modeling has yielded only modest progress, primarily due to a lack of situation-aware deployment. Data-driven Reynolds-averaged Navier–Stokes (ML-RANS) closures frequently fail to generalize across diverse flow regimes, while scale-resolving simulations (SRS) remain computationally prohibitive. As a result, ML-RANS is often misapplied outside its domain of validity, and ML-SRS is unnecessarily deployed on flows fully amenable to RANS. To guide optimal AI/ML deployment, we propose a turbulence taxonomy map parameterized by degrees of freedom () and the degree of non-equilibrium (). By applying Weaver's well-recognized complexity framework, we classify turbulence into distinct physical regimes. This categorization identifies where local ML-RANS surrogates can generalize, clarifies where explicit scale resolution is physically mandatory, and highlights where physics-informed neural networks (PINNs) are most effective. Ultimately, this perspective establishes a physics-grounded framework for the flow-aware, successful deployment of AI/ML in turbulence.
cs.LG
We present ContinuousCloth, a continuous-time, physics-informed neural solver for deformable cloth dynamics that enforces a spring–mass ODE within a neural trajectory model. Unlike classical time-stepping simulators that return trajectories only on a discrete integration grid, ContinuousCloth supports querying at arbitrary timestamps and computing displacement, velocity, and acceleration via automatic differentiation. We evaluate ContinuousCloth along two dimensions. In a physics-only setting, ContinuousCloth achieves trajectory accuracy comparable to high-precision solvers across six diverse boundary-condition scenarios while reducing runtime by up to 17.4 times. When fused with sparse and noisy observations, the spring–mass ODE acts as a strong inductive bias for downstream tasks: interpolation and parameter estimation. That is, ContinuousCloth reduces interpolation error by 7.3 times over a data-only neural baseline in simulation and 2.4 times on real-world cloth sequences, and achieves 2.6 times lower parameter error than a differentiable-solver baseline under high-noise conditions, demonstrating consistent robustness under realistic measurement imperfections.