Physics-Informed ML

ML: Machine Learning

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60 papers in the last four weeks, up 131% on the four weeks before. 0.6% of all new papers.

Jul 13Week of Sep 28

Latest papers 561

Nov 19, 2025math.NA

Neural network-driven domain decomposition for efficient solutions to the Helmholtz equation

Accurately simulating wave propagation is crucial in fields such as acoustics, electromagnetism, and seismic analysis. Traditional numerical methods, like finite difference and finite element approaches, are widely used to solve governing partial differential equations (PDEs) such as the Helmholtz equation. However, these methods face significant computational challenges when applied to high-frequency wave problems in complex two-dimensional domains. This work investigates Finite Basis Physics-Informed Neural Networks (FBPINNs) and their multilevel extensions as a promising alternative. These methods leverage domain decomposition, partitioning the computational domain into overlapping sub-domains, each governed by a local neural network. We assess their accuracy and computational efficiency in solving the Helmholtz equation for the homogeneous case, demonstrating their potential to mitigate the limitations of traditional approaches.

Victorita Dolean, Daria Hrebenshchykova, Stéphane Lanteri +1

Department of Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands · Atlantis project-team, Inria Research Center at Université Côte d’Azur, France · MACARON project-team, Université de Strasbourg, CNRS, Inria, IRMA, France

Neural PDE Solvers PDE Solving Physics-Informed ML

Nov 8, 2025cs.LG

Hard-constraint physics-residual networks for hydrogen crossover prediction and high-pressure extrapolation in PEM water electrolysis

Hydrogen crossover is a critical safety and efficiency constraint in high-pressure polymer electrolyte membrane water electrolysis (PEMWE), but accurate prediction remains difficult because data are limited, transport physics are strongly coupled, and industrial operation requires reliable extrapolation beyond observed conditions. This study develops a hard-constraint physics-residual network (PR-Net) for hydrogen crossover prediction in PEMWE and compares it with a purely data-driven neural network (NN) and a soft-constraint physics-informed neural network (PINN). PR-Net embeds Henry's, Fick's, and Faraday's laws as a deterministic backbone and learns only a residual correction for unmodelled nonlinear effects. The benchmark includes 184 observations from eight peer-reviewed sources across six membrane types, covering 1-200 bar,

25-85°C

, and

0.05-5.0 A cm^{-2}

. PR-Net achieves

R^2 = 99.57 \pm 0.16%

, with 9-fold lower prediction variability than NN and PINN. In pressure-axis extrapolation, PR-Net attains

R^2 = 94.02 \pm 0.92%

at 200 bar, 2.5 times beyond the training pressure range, compared with

68.06 \pm 5.52%

for PINN and

58.00 \pm 8.60%

for NN (p < 0.001). Residual analysis indicates that the learned correction captures part of the high-pressure gas-phase non-ideality and recovers a transport-regime transition near

0.23 A cm^{-2}

between Fickian diffusion-dominated and Faradaic production-dominated transport. With a computation time of

1.08 \pm 0.34 ms

on low-power embedded hardware, PR-Net provides a practical framework for real-time crossover monitoring, adaptive process control, and safer high-pressure green-hydrogen operation.

Yong-Woon Kim, Jihyeok Lee, Chulung Kang +1

Department of Computer Engineering, Jeju National University, Jeju, 63243, South Korea · Faculty of Applied Energy System, Jeju National University, Jeju, 63243, South Korea · Department of Mechanical System Engineering, Jeju National University, Jeju, 63243, South Korea +1

Neural Surrogate Modeling Physics-Informed ML

Nov 1, 2025cs.SD

Physics-Informed Neural Networks for Speech Production

The analysis of speech production based on physical models of the vocal folds and vocal tract is essential for studies on vocal-fold behavior and linguistic research. This paper proposes a speech production analysis method using physics-informed neural networks (PINNs). The networks are trained directly on the governing equations of vocal-fold vibration and vocal-tract acoustics. Vocal-fold collisions introduce nondifferentiability and vanishing gradients, challenging phenomena for PINNs. We demonstrate, however, that introducing a differentiable approximation function enables the analysis of vocal-fold vibrations within the PINN framework. The period of self-excited vocal-fold vibration is generally unknown. We show that by treating the period as a learnable network parameter, a periodic solution can be obtained. Furthermore, by implementing the coupling between glottal flow and vocal-tract acoustics as a hard constraint, glottis-tract interaction is achieved without additional loss terms. We confirmed the method's validity through forward and inverse analyses, demonstrating that the glottal flow rate, vocal-fold vibratory state, and subglottal pressure can be simultaneously estimated from speech signals. Notably, the same network architecture can be applied to both forward and inverse analyses, highlighting the versatility of this approach. The proposed method inherits the advantages of PINNs, including mesh-free computation and the natural incorporation of nonlinearities, and thus holds promise for a wide range of applications.

Kazuya Yokota, Ryosuke Harakawa, Masaaki Baba +1

Department of Mechanical Engineering, Nagaoka University of Technology, 1603-1, Kamitomioka, Nagaoka, Niigata, Japan · Department of Electrical, Electronics and Information Engineering, Nagaoka University of Technology

Speech Processing Physics-Informed ML Inverse Problems

Oct 29, 2025cs.LG

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries

Initial-boundary value problems (IBVPs) provide the essential framework for modelling a wide range of phenomena in physics and engineering. We introduce a novel method for efficiently solving IBVPs using Lie symmetries to enforce the associated partial differential equation (PDE) exactly by construction. By leveraging symmetry transformations, our model embeds the underlying physical laws and learns the solution solely from initial and boundary data. Consequently, the boundary loss directly quantifies domain-wide error, enabling rigorous error estimation for well-posed IBVPs. We implement LieSolver and demonstrate its application to linear homogeneous PDEs, showing that it outperforms physics-informed neural networks (PINNs) in both speed and accuracy while yielding compact models. Overall, our approach significantly enhances the efficiency and reliability of predictions for PDE-constrained problems.

René P. Klausen, Ivan Timofeev, Jonas Naujoks +4

Department of Artificial Intelligence, Fraunhofer Heinrich Hertz Institute, Berlin, Germany · Department of Electrical Engineering and Computer Science, Technische Universität Berlin, Germany · BIFOLD Berlin Institute for the Foundations of Learning and Data, Berlin, Germany +1

Neural PDE Solvers PDE Solving Physics-Informed ML

Oct 16, 2025stat.ML

Inverse Problem for Partial Differential Equations with Jump Discontinuities in Coefficients by Two-stage Physics-Informed Deep Learning and Statistical Mixture Models

This work proposes a two-stage physics-informed deep learning framework that combines neural-network-based sampling with statistical inference and constrained parameter refinement. In the first stage, a dual-network physics-informed architecture is used, where a main-network approximates the PDE solution and an auxiliary coefficient sub-network provides a relaxed continuous soft approximation of the true discontinuous coefficient field. A gradient-adaptive weighting strategy is incorporated to improve residual training and enhance sampling reliability near possible discontinuity regions. The sampled coefficient values are then analyzed using Bayesian learning for Gaussian mixture models and birth-death Markov chain model selection, which identify the number of coefficient regimes and provide candidate intervals for coefficient values and transition regions. In the second stage, the inverse problem is reformulated as a constrained physics-informed estimator, in which the coefficient is replaced by a form-consistent hard approximation explicitly represented as a piecewise-constant function over the spatiotemporal domain. Comprehensive numerical experiments on PDEs with jump-discontinuous coefficients demonstrate that the proposed framework achieves adaptability and accurate parameter identification with acceptable computational costs compared to existing methods. Applications to solution reconstruction further illustrate its practical potential. This work provides a generalizable computational approach for inverse problems governed by PDEs with discontinuous parameter structures, particularly in non-stationary and heterogeneous systems.

Zhikun Zhang, Guanyu Pan, Xiangjun Wang +2

School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072, China · School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China · SandGold AI Research, Guangzhou 510642, China +3

Bayesian Mixture Models Physics-Informed ML PDE Inverse Problems

Oct 2, 2025cs.LG

Neural non-canonical Hamiltonian dynamics for long-time simulations

This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes. Previous research focused on either facet, respectively with a potential-based architecture and with degenerate variational integrators, but new issues arise when combining both. In experiments, the learnt model is sometimes numerically unstable due to the gauge dependency of the scheme, rendering long-time simulations impossible. In this paper, we identify this problem and propose two different training strategies to address it, either by directly learning the vector field or by learning a time-discrete dynamics through the scheme. Several numerical test cases assess the ability of the methods to learn complex physical dynamics, like the guiding center from gyrokinetic plasma physics.

Clémentine Courtès, Emmanuel Franck, Michael Kraus +2

IRMA, MACARON · Institut de Recherche Mathématique Avancée, UMR 7501 Université de Strasbourg et CNRS, 7 rue René Descartes 672000 Strasbourg, France. · INRIA Nancy-Grand Est, MACARON Project, Strasbourg, France. +5

Dynamical Systems Nonlinear System Identification Hamiltonian Neural Networks Physics-Informed ML Hamiltonian Dynamics

Sep 28, 2025cs.RO

MAD-PINN: A Decentralized Physics-Informed Machine Learning Framework for Safe and Optimal Multi-Agent Control

Co-optimizing safety and performance in large-scale multi-agent systems remains a fundamental challenge. Existing approaches based on multi-agent reinforcement learning (MARL), safety filtering, or Model Predictive Control (MPC) either lack strict safety guarantees, suffer from conservatism, or fail to scale effectively. We propose MAD-PINN, a decentralized physics-informed machine learning framework for solving the multi-agent state-constrained optimal control problem (MASC-OCP). Our method leverages an epigraph-based reformulation of SC-OCP to simultaneously capture performance and safety, and approximates its solution via a physics-informed neural network. Scalability is achieved by training the SC-OCP value function on reduced-agent systems and deploying them in a decentralized fashion, where each agent relies only on local observations of its neighbours for decision-making. To further enhance safety and efficiency, we introduce an Hamilton-Jacobi (HJ) reachability-based neighbour selection strategy to prioritize safety-critical interactions, and a receding-horizon policy execution scheme that adapts to dynamic interactions while reducing computational burden. Experiments on multi-agent navigation tasks demonstrate that MAD-PINN achieves superior safety-performance trade-offs, maintains scalability as the number of agents grows, and consistently outperforms state-of-the-art baselines.

Manan Tayal, Aditya Singh, Shishir Kolathaya +1

Center for Cyber-Physical Systems, Indian Institute of Science, Bangalore, India · Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, USA · Department of Aeronautics and Astronautics, Stanford University, USA

Multi-Agent Control Constrained Optimization Physics-Informed ML

Sep 26, 2025cs.LG

Physics-informed GNN for medium-high voltage AC power flow with edge-aware attention and line search correction operator

Physics-informed graph neural networks (PIGNNs) have emerged as fast AC power-flow solvers that can replace the classic NewtonRaphson (NR) solvers, especially when thousands of scenarios must be evaluated. However, current PIGNNs still need accuracy improvements at parity speed; in particular, the soft constraint on the physics loss is inoperative at inference, which can deter operational adoption. We address this with PIGNN-Attn-LS, combining an edge-aware attention mechanism that explicitly encodes line physics via per-edge biases to form a fully differentiable knownoperator layer inside the computation graph, with a backtracking line-search-based globalized correction operator that restores an operative decrease criterion at inference. Training and testing use a realistic High-/Medium-Voltage scenario generator, with NR used only to construct reference states. On held-out HV cases consisting of 4-32-bus grids, PIGNN-Attn-LS achieves a test RMSE of 0.00033 p.u. in voltage and 0.08 deg in angle, outperforming the PIGNN-MLP baseline by 99.5% and 87.1%, respectively. With streaming micro-batches, it delivers 2-5x faster batched inference than NR on 4-1024-bus grids.

Changhun Kim, Timon Conrad, Redwanul Karim +6

Pattern Recognition Lab, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany · Institute of Electrical Energy Systems, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany

Efficient Neural Network Inference Graph Attention Networks Physics-Informed ML Physics-Informed GNNs Power Systems

Sep 19, 2025math.NA

A Flow-rate-conserving CNN-based Domain Decomposition Method for Blood Flow Simulations

This work aims to predict blood flow with non-Newtonian viscosity in stenosed arteries using convolutional neural network (CNN) surrogate models. An alternating Schwarz domain decomposition method is proposed which uses CNN-based subdomain solvers. A universal subdomain solver (USDS) is trained on a single, fixed geometry and then applied for each subdomain solve in the Schwarz method. Results for two-dimensional stenotic arteries of varying shape and length for different inflow conditions are presented and statistically evaluated. One key finding, when using a limited amount of training data, is that incorporating a physics-aware constraint, as, in our case, flow rate conservation, into the USDS improves the prediction accuracy and convergence behavior of the Schwarz method compared to a purely data-driven USDS. As the USDS is a data-driven, inexact subdomain solver, admissible parameter ranges for the geometry and inflow configurations must be defined and tested.

Simon Klaes, Axel Klawonn, Natalie Kubicki +4

Department of Mathematics and Computer Science, University of Cologne, Germany · Center for Data and Simulation Science, University of Cologne, Germany · Institute for Advanced Simulation (IAS-2), Forschungszentrum Jülich, Germany +1

PDE Solving PDE Surrogate Modeling Physics-Informed ML Convolutional Neural Networks Computational Fluid Dynamics

Aug 29, 2025cs.LG

Convergence of Stochastic Gradient Methods for Wide Two-Layer Physics-Informed Neural Networks for the Poisson Equation

Physics informed neural networks (PINNs) represent a very popular class of neural solvers for partial differential equations. In practice, one often employs stochastic gradient descent type algorithms to train the neural network. Therefore, the convergence guarantee of stochastic gradient descent is of fundamental importance. In this work, we establish the linear convergence of stochastic gradient descent / flow in training over-parameterized two layer PINNs with a general class of activation functions for solving one model second-order elliptic problem, i.e., the Poisson equation, in the sense of high probability. These results extend the existing result [20] in which gradient descent was analyzed. The challenge of the analysis lies in handling the dynamic randomness introduced by stochastic optimization methods. The key of the analysis lies in ensuring the positive definiteness of suitable Gram matrices during the training. The analysis sheds insight into the dynamics of the optimization process, and provides guarantees on physics informed neural networks trained by stochastic algorithms.

Bangti Jin, Longjun Wu

Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, P.R. China

Neural PDE Solvers PDE Solving Stochastic Optimization Convergence Physics-Informed ML Stochastic Gradient Descent

Aug 25, 2025cs.CV

InSituRes: A Physics-Informed Same-Grid Model for Enhanced Dynamic X-ray Micro-CT Reconstructions

X-ray micro-computed tomography (micro-CT) provides non-destructive three-dimensional (3D) imaging of porous material microstructures. In situ experiments, including mechanical loading and reactive transport, increasingly require dynamic four-dimensional (4D) imaging with volumes repeatedly acquired during experiments. However, rapid acquisition typically requires fewer projections, shorter exposures, or reduced fields of view, producing reconstructions with noise, blur, and artifacts that obscure pores, microcracks, and interfaces. To address this challenge, this study introduces InSituRes, a physics-informed same-grid volumetric enhancement framework for fast dynamic X-ray micro-CT imaging of temporally evolving materials. InSituRes maps fast-acquisition volumes to higher-quality long-acquisition reconstructions using paired scans of the same specimens. The model integrates 3D convolutional feature extraction with slice-wise transformer attention to capture local and broader in-plane context. A learnable forward degradation model approximates rapid acquisition effects, including spatial blurring, intensity scaling differences, and signal-dependent noise. During training, reconstructed volumes should match high-quality reference scans and reproduce observed fast acquisition data after propagation through the forward model, imposing a physics-guided consistency constraint. Experiments on unseen micro-CT datasets demonstrate improved reconstruction fidelity and enhanced visibility of fine microstructural features relative to conventional interpolation and learning-based enhancement approaches. The framework supports quantitative interpretation of fast 4D X-ray micro-CT scans of evolving materials.

Qinyi Tian, Andrea Bisciotti, Soniya Tiwari +2

Department of Civil & Environmental Engineering, Duke University, Durham, North Carolina, 27708, USA · Department of Physics and Earth Sciences, University of Ferrara, Via Saragat 1, Ferrara 44141, Italy · Department of Mechanical Engineering & Materials Science, Duke University, Durham, North Carolina, 27708, USA

Image Restoration Physics-Informed ML Computed Tomography

Aug 5, 2025cs.LG

Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems

We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a differentiable post-training procedure that minimizes weak-form residuals of governing partial differential equations (PDEs), promoting physical consistency and adherence to boundary conditions without distorting the underlying learned distribution. To infer unknown physical inputs, such as source terms, material parameters, or boundary data, we augment the generative process with a learnable latent parameter predictor and propose a joint optimization strategy. The resulting model produces physically valid field solutions alongside plausible estimates of hidden parameters, effectively addressing ill-posed inverse problems in a data-driven yet physicsaware manner. We validate our method on canonical PDE benchmarks, demonstrating improved satisfaction of PDE constraints and accurate recovery of latent coefficients. Our approach bridges generative modelling and scientific inference, opening new avenues for simulation-augmented discovery and data-efficient modelling of physical systems.

Jan Tauberschmidt, Sophie Fellenz, Sebastian J. Vollmer +1

DSA, German Research Center for Artificial Intelligence (DFKI) · Department of Computer Science, University of Kaiserslautern–Landau (RPTU) · Department of Mathematics, Imperial College London

Physics-Informed Generative Modeling Flow Matching Generative Modeling Physics-Informed ML PDE Inverse Problems

Jun 23, 2025math.NA

DPG loss functions for learning parameter-to-solution maps by neural networks

We develop, analyze, and experimentally explore residual-based loss functions for machine learning of parameter-to-solution maps in the context of parameter-dependent families of partial differential equations (PDEs). Our primary concern is on rigorous accuracy certification to enhance the prediction capability of the resulting deep neural network reduced models. This is achieved by the use of variationally correct loss functions. Through one specific example of an elliptic PDE, details for establishing the variational correctness of a loss function from an ultraweak Discontinuous Petrov Galerkin (DPG) discretization are worked out. Despite the focus on the example, the proposed concepts apply to a much wider scope of problems, namely problems for which stable DPG formulations are available. The issue of high-contrast diffusion fields and ensuing difficulties with degrading ellipticity are discussed. Both numerical results and theoretical arguments illustrate that for high-contrast diffusion parameters the proposed DPG loss functions deliver much more robust performance than simpler least-squares losses.

Pablo Cortés Castillo, Wolfgang Dahmen, Jay Gopalakrishnan

PDE Solving PDE Surrogate Modeling Robust Loss Functions PDE Operator Learning Physics-Informed ML

Jun 23, 2025cs.LG

GeNeRT: A Physics-Informed Approach to Intelligent Wireless Channel Modeling via Generalizable Neural Ray Tracing

Neural ray tracing (RT) has emerged as a promising paradigm for channel modeling by integrating physical propagation principles with neural networks. However, existing neural RT methods remain limited by strong spatial dependence and weak adherence to electromagnetic laws. We propose GeNeRT, a generalizable neural RT framework that improves generalization and accuracy through relative geometric features, scatterer semantics, and a Fresnel-inspired polarization-driven architecture. GeNeRT is trained through a three-stage strategy: polarization-specific module-wise pre-training captures general ray-surface interaction behavior; system-wise end-to-end training uses only receiver-side channel impulse responses to learn site-specific propagation characteristics; and measurement-based fine-tuning employs sparse measured multipath components (MPCs) to adapt polarization-related modules to real-world environments. Extensive outdoor simulations demonstrate robust intra-scenario transferability and inter-scenario zero-shot generalization. In an unseen scenario, GeNeRT achieves an overall error of

-35.36

dB and an average-delay error of 4.91 ns, compared with

-10.85

dB and 32.38 ns for the best baseline. With only 75 measured reflected MPCs, fine-tuning further reduces the overall error from

-14.48

to

-22.90

dB and the average-delay error from 6.28 to 3.58 ns. Ablation studies confirm the effectiveness of the proposed architecture and training strategy.

Kejia Bian, Meixia Tao, Shu Sun +2

School of Information Science and Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China · Shanghai Innovation Institute, Shanghai 200231, China

Neural Network Generalization Wireless Communications Radio Propagation Modeling Physics-Informed ML

Jun 18, 2025cs.LG

Interpretability and Generalization Bounds for Learning Spatial Physics

While there are many applications of ML to scientific problems that look promising, visuals can be deceiving. Using numerical analysis techniques, we rigorously quantify the accuracy, convergence rates, and generalization bounds of certain ML models applied to linear differential equations for parameter discovery or solution finding. Beyond the quantity and discretization of data, we identify that the function space of the data is critical to the generalization of the model. A similar lack of generalization is empirically demonstrated for commonly used models, including physics-specific techniques. Counterintuitively, we find that different classes of models can exhibit opposing generalization behaviors. Based on our theoretical analysis, we also introduce a new mechanistic interpretability lens on scientific models whereby Green's function representations can be extracted from the weights of black-box models. Our results inform a new cross-validation technique for measuring generalization in physical systems, which can serve as a benchmark.

Alejandro Francisco Queiruga, Theo Gutman-Solo, Shuai Jiang

OpenAI, San Francisco, CA, USA · Google, Mountain View, CA, USA · Sandia National Laboratories, Albuquerque, NM, USA

Neural Network Generalization Mechanistic Interpretability Scientific ML Physics-Informed ML Generalization Bounds

May 28, 2025cs.LG

Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation

Modeling physical systems in a generative manner offers several advantages, including the ability to handle partial observations, generate diverse solutions, and address both forward and inverse problems. Recently, diffusion models have gained increasing attention in the modeling of physical systems, particularly those governed by partial differential equations (PDEs). However, diffusion models only access noisy data

\boldsymbol{x}_t

at intermediate steps, making it infeasible to directly enforce constraints on the clean sample

\boldsymbol{x}_0

at each noisy level. As a workaround, constraints are typically applied to the expectation of clean samples

\mathbb{E}[\boldsymbol{x}_0|\boldsymbol{x}_t]

, which is estimated using the learned score network. However, imposing PDE constraints on the expectation does not strictly represent the one on the true clean data, known as Jensen's Gap. This gap creates a trade-off: enforcing PDE constraints may come at the cost of reduced accuracy in generative modeling. To address this, we propose a simple yet effective post-hoc distillation approach, where PDE constraints are not injected directly into the diffusion process, but instead enforced during a post-hoc distillation stage. We term our method as Physics-Informed Distillation of Diffusion Models (PIDDM). This distillation not only facilitates single-step generation with improved PDE satisfaction, but also support both forward and inverse problem solving and reconstruction from randomly partial observation. Extensive experiments across various PDE benchmarks demonstrate that PIDDM significantly improves PDE satisfaction over several recent and competitive baselines, such as PIDM, DiffusionPDE, and ECI-sampling, with less computation overhead. Our approach can shed light on more efficient and effective strategies for incorporating physical constraints into diffusion models.

Yi Zhang, Peng Wang, Difan Zou

Institute of Data Science · Department of Computer and Information Science · Institute of Data Science & School of Computing and Data Science

Physics-Informed Diffusion Models Diffusion Model Distillation Generative Modeling Physics-Informed ML PDE Inverse Problems

May 16, 2025math.NA

Accelerating Natural Gradient Descent for PINNs with Randomized Numerical Linear Algebra

Natural Gradient Descent (NGD) has emerged as a promising optimization algorithm for training neural network-based solvers for partial differential equations (PDEs), such as Physics-Informed Neural Networks (PINNs). However, its practical use is often limited by the high computational cost of solving linear systems involving the Gramian matrix. While matrix-free NGD methods based on the conjugate gradient (CG) method avoid explicit matrix inversion, the ill-conditioning of the Gramian significantly slows the convergence of CG. In this work, we extend matrix-free NGD to broader classes of problems than previously considered and propose the use of Randomized Numerical Linear Algebra (RandNLA) techniques for efficient preconditioning of the inner CG solver. The resulting algorithms demonstrate substantial performance improvements over existing NGD-based methods on a range of PDE problems discretized using neural networks, and offer competitive results compared to other state-of-the-art optimizers.

Ivan Bioli, Carlo Marcati, Giancarlo Sangalli

Department of Mathematics, University of Pavia, Via A. Ferrata 5, 27100 Pavia, Italy · Department of Civil Engineering and Architecture, University of Pavia, Via A. Ferrata 3, 27100 Pavia, Italy · Istituto di Matematica Applicata e Tecnologie Informatiche “E. Magenes”, CNR, Via A. Ferrata 1, 27100 Pavia, Italy

Neural PDE Solvers Gradient Descent Physics-Informed ML

May 6, 2025stat.ML

Physics-Informed Sylvester Normalizing Flows for Bayesian Inference in Magnetic Resonance Spectroscopy

Magnetic resonance spectroscopy (MRS) is a non-invasive technique to measure the metabolic composition of tissues, offering valuable insights into neurological disorders, tumor detection, and other metabolic dysfunctions. However, accurate metabolite quantification is hindered by challenges such as spectral overlap, low signal-to-noise ratio, and various artifacts. Traditional methods like linear-combination modeling are susceptible to ambiguities and commonly only provide a theoretical lower bound on estimation accuracy in the form of the Cramér-Rao bound. This work introduces a Bayesian inference framework using Sylvester normalizing flows (SNFs) to approximate posterior distributions over metabolite concentrations, enhancing quantification reliability. A physics-based decoder incorporates prior knowledge of MRS signal formation, ensuring realistic distribution representations. We validate the method on simulated 7T proton MRS data, demonstrating accurate metabolite quantification, well-calibrated uncertainties, and insights into parameter correlations and multi-modal distributions.

Julian P. Merkofer, Dennis M. J. van de Sande, Alex A. Bhogal +1

Eindhoven University of Technology, Eindhoven, The Netherlands · University Medical Center Utrecht, Utrecht, The Netherlands

Normalizing Flows Bayesian Inference Physics-Informed ML

Mar 24, 2025cs.LG

Residuals Are Not Enough: Limits of Physics-Informed Pre-Training for Scientific Foundation Models

Scientific foundation models (SciFMs) aim to learn generalizable representations of physical systems governed by partial differential equations (PDEs), enabling transfer across tasks and domains. While physics-informed methods, which leverage PDE residuals as supervisory signals, have shown promise in scientific machine learning (SciML) for improving accuracy and reducing data requirements, their potential in the context of SciFMs remains relatively unexplored. In this evaluation study, we investigate whether (and how) physics-informed pre-training improves the generalization, robustness, and data efficiency of SciFMs. We conduct systematic experiments across a diverse set of PDEs, ranging from simple problems with periodic boundary conditions to more challenging systems such as the Navier-Stokes equations and non-periodic geometries. Our results show that physics-informed pre-training provides clear benefits in

nice,'' e.g., structured, well-aligned settings: it enhances generalization and reduces data dependence, compared to data-only pre-training. However, these advantages diminish significantly as the downstream tasks become

harder,'' e.g., as they involve discontinuities or deviate from the pre-training distribution. In complex or structurally different problems, such as those involving new boundary conditions or PDE operators, physics-informed models may perform only on par with---or even worse---than data-driven baselines. While residual-based pre-training helps in idealized regimes, realizing broadly transferable SciFMs will likely require subtler spatiotemporal inductive biases and more principled integration of physical knowledge into model architectures.

Serge Kotchourko, Amin Totounferoush, Michael W. Mahoney +1

University of Stuttgart, Germany · ICSI, LBNL, and University of California, Berkeley, USA

PDE Surrogate Modeling Physics-Informed ML

Mar 3, 2025eess.IV

Hyperspectral Image Restoration and Super-resolution with Physics-Aware Deep Learning for Biomedical Applications

Hyperspectral imaging is a powerful bioimaging tool which can uncover novel insights, thanks to its sensitivity to the intrinsic properties of materials. However, this enhanced contrast comes at the cost of system complexity, constrained by an inherent trade-off between spatial, spectral, and temporal resolution. To overcome this limitation, we present a self-supervised deep learning-based approach that restores and enhances pixel resolution post-acquisition without requiring external training data beyond the images to be restored. Fine-tuned using metrics aligned with the imaging model, our physics-aware method achieves a 16

\times

pixel super-resolution enhancement and a 12

\times

imaging speedup without the need of additional training data for transfer learning. Applied to both synthetic and experimental data from five different sample types, including healthy and diseased tissues, we demonstrate that the model preserves biological integrity, as we did not detect systematic loss of biological features or biologically consequential hallucinations in tested datasets. We also concretely demonstrate the model's ability to reveal disease-associated metabolic changes that would otherwise remain undetectable. Furthermore, we provide physical insights into the model's inner workings, paving the way for future refinements that could potentially reveal novel high resolution features in an explainable manner. All methods are available as open-source software on GitHub.

Yuchen Xiang, Zhaolu Liu, Monica Emili Garcia-Segura +12

Department of Metabolism, Digestion and Reproduction, Imperial College London, London, UK · Department of Mathematics, Imperial College London, London, UK · Department of Clinical Neurosciences and NIHR Biomedical Research Centre, University of Cambridge, Cambridge, UK +4

Self-Supervised Learning Physics-Guided Image Restoration Hyperspectral Image Super-Resolution Hyperspectral Imaging Image Restoration Physics-Informed ML

Feb 16, 2025quant-ph

Physics-Informed Support Vector Kernels via Green-Function Analogies and Jackson-Chebyshev Spectral Design

Kernel selection for regression of physical observables is often heuristic. We investigate a physics-informed strategy in which functional forms and spectral structures associated with Green's functions motivate kernel selection without requiring an exact identification between a machine-learning kernel and a physical propagator. The principal construction is a Jackson-damped Chebyshev kernel inspired by the kernel polynomial method (KPM); its explicit feature map yields a positive-semidefinite Gram matrix by construction and provides an inspectable spectral prior for structured observables. We evaluate standard and custom SVR models on copper-conductivity proxies, local Dirac-like band dispersion, quartic-oscillator energy levels, photonic-crystal transmission, and Fibonacci-chain transmission using repeated nested validation, learning curves, random-forest and multilayer-perceptron baselines, and low-rank Nyström tests where relevant. The framework is intended for finite-data regression of precomputed observables while boundary conditions remain part of the physical model that generates those observables.

Nan-Hong Kuo, Renata Wong

Department of Physics, National Taiwan University, Taipei, Taiwan · Department of Artificial Intelligence, Chang Gung University, Taoyuan, Taiwan · Department of Neurology, Chang Gung Memorial Hospital, Keelung, Taiwan +1

Support Vector Machines Kernel Methods Physics-Informed ML Spectral Methods