Physics-Informed ML

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93 papers in the last four weeks, up 26% on the four weeks before. 0.6% of all new papers.

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Convergence of Stochastic Gradient Methods for Wide Two-Layer Physics-Informed Neural Networks for the Poisson Equation
Aug 29, 2025Bangti Jin, Longjun WuNeural PDE Solvers PDE Solving
Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, P.R. China
InSituRes: A Physics-Informed Same-Grid Model for Enhanced Dynamic X-ray Micro-CT Reconstructions
Aug 25, 2025Qinyi Tian, Andrea Bisciotti, Soniya Tiwari +2Image Restoration Physics-Informed ML
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
Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems
Aug 5, 2025Jan Tauberschmidt, Sophie Fellenz, Sebastian J. Vollmer +1Physics-Informed Generative Modeling Flow Matching
DSA, German Research Center for Artificial Intelligence (DFKI) · Department of Computer Science, University of Kaiserslautern–Landau (RPTU) · Department of Mathematics, Imperial College London
DPG loss functions for learning parameter-to-solution maps by neural networks
Jun 23, 2025Pablo Cortés Castillo, Wolfgang Dahmen, Jay GopalakrishnanPDE Solving PDE Surrogate Modeling
GeNeRT: A Physics-Informed Approach to Intelligent Wireless Channel Modeling via Generalizable Neural Ray Tracing
Jun 23, 2025Kejia Bian, Meixia Tao, Shu Sun +2Neural Network Generalization Wireless Communications
School of Information Science and Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China · Shanghai Innovation Institute, Shanghai 200231, China
Interpretability and Generalization Bounds for Learning Spatial Physics
Jun 18, 2025Alejandro Francisco Queiruga, Theo Gutman-Solo, Shuai JiangNeural Network Generalization Mechanistic Interpretability
OpenAI, San Francisco, CA, USA · Google, Mountain View, CA, USA · Sandia National Laboratories, Albuquerque, NM, USA
Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation
May 28, 2025Yi Zhang, Peng Wang, Difan ZouPhysics-Informed Diffusion Models Diffusion Model Distillation
Institute of Data Science · Department of Computer and Information Science · Institute of Data Science & School of Computing and Data Science
Accelerating Natural Gradient Descent for PINNs with Randomized Numerical Linear Algebra
May 16, 2025Ivan Bioli, Carlo Marcati, Giancarlo SangalliNeural PDE Solvers Gradient Descent
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
Physics-Informed Sylvester Normalizing Flows for Bayesian Inference in Magnetic Resonance Spectroscopy
May 6, 2025Julian P. Merkofer, Dennis M. J. van de Sande, Alex A. Bhogal +1Normalizing Flows Bayesian Inference
Eindhoven University of Technology, Eindhoven, The Netherlands · University Medical Center Utrecht, Utrecht, The Netherlands
Residuals Are Not Enough: Limits of Physics-Informed Pre-Training for Scientific Foundation Models
Mar 24, 2025Serge Kotchourko, Amin Totounferoush, Michael W. Mahoney +1PDE Surrogate Modeling Physics-Informed ML
University of Stuttgart, Germany · ICSI, LBNL, and University of California, Berkeley, USA
Hyperspectral Image Restoration and Super-resolution with Physics-Aware Deep Learning for Biomedical Applications
Mar 3, 2025Yuchen Xiang, Zhaolu Liu, Monica Emili Garcia-Segura +12Self-Supervised Learning Physics-Guided Image Restoration
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
Physics-Informed Support Vector Kernels via Green-Function Analogies and Jackson-Chebyshev Spectral Design
Feb 16, 2025Nan-Hong Kuo, Renata WongSupport Vector Machines Kernel Methods
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

Aug 29, 2025, cs.LGJ/K move · Enter open · S save

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

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

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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.

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