Physics-Informed ML

ML: Machine Learning

Physics-informed machine learning studies how to combine observations with governing equations, conservation laws, symmetries, and other scientific knowledge. Common approaches include physics-informed neural networks (PINNs) that penalize equation residuals, weak or variational formulations, neural operators for families of PDE solutions, and hybrid models that learn corrections to mechanistic simulators. These methods are used for forward simulation, inverse problems, parameter estimation, forecasting, and fast surrogates when measurements or computational resources are limited. A central challenge is that physical constraints can improve data efficiency and consistency but can also hinder training or harm predictions when the equations, discretization, or assumed structure do not match the system.

Latest papers

843 papers75 papers in the last four weeks, down 13% on the four weeks before. 0.4% of all new papers.

Leveraging Differentiable PDE Solvers for Semi-Neural Spatial Reconstruction From Sparse Measurements
Jan 28, 2026Ofek Aloni, Barak FishbainDifferentiable Physics Physics-Informed ML
Department of Mathematics, Technion, Israel · Department of Civil and Environmental Engineering, Technion, Israel
Adaptively trained Physics-informed Radial Basis Function Neural Networks for Solving Multi-asset Option Pricing Problems
Jan 19, 2026Yan Ma, Yumeng Ren, Elisabeth LarssonQuantitative Finance PDE Solving
aCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou, China · bDepartment of Mathematics, City University of Hong Kong, Hong Kong SAR, China · cDepartment of Information Technology, Uppsala University, Sweden
Disentangling Aleatoric and Epistemic Uncertainty in Physics-Informed Neural Networks. Application to Insulation Material Degradation Prognostics
Jan 7, 2026Ibai Ramirez, Jokin Alcibar, Joel Pino +2Bayesian Neural Networks Uncertainty Quantification
Department of Electronics and Computer Science Mondragon University Arrasate-Mondragon, 20500, Spain · CARTIF Technology Centre Valladolid, 47151, Spain · Department of Physical Chemistry University of the Basque Country (EHU)[cs.LG] Basque Centre for Applied Mathematics (BCAM) Leioa, 20018, Spain +1
Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learning
Jan 1, 2026Abhisek Ganguly, Santosh Ansumali, Sauro SucciDynamical Systems Neural PDE Solvers
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore, 560064, Karnataka, India · Italian Institute of Technology, Viale Regina Elena 291, 00161 Rome, Italy · University of Roma Tre, Italy +2
Evolutionary Physics-Informed Temporal Fusion for Lane-Change Intention Prediction
Dec 30, 2025Jiazhao Shi, Qiyang Xie, Ziyu Wang +7Autonomous Driving Physics-Informed ML
Tandon School of Engineering New York University New York, USA · Khoury College of Computer Science Northeastern University Boston, USA · School of Business Wake Forest University Winston Salem, USA +6
KIGNet: Physics-Motivated Multi-Graph Representation Learning for Explainable Jet Tagging
Dec 8, 2025Md Raqibul Islam, Adrita Khan, Mir Sazzat Hossain +6Graph Representation Learning Jet Tagging
Center for Computational & Data Sciences, Independent University, Bangladesh, Dhaka-1229, Bangladesh · Department of Theoretical Physics, University of Dhaka, Dhaka-1000, Bangladesh · Department of Physical Sciences, Independent University, Bangladesh, Dhaka-1229, Bangladesh
Quantum-Classical Physics-Informed Neural Networks for Solving Reservoir Seepage Equations
Dec 3, 2025Xiang Rao, Yina Liu, Yuxuan ShenPDE Solving Physics-Informed ML
School of Petroleum Engineering, Yangtze University, Wuhan 430100, China · College of Future Technology, Yangtze University, Wuhan 430100, China · State Key Laboratory of Low Carbon Catalysis and Carbon Dioxide Utilization (Yangtze University), Wuhan 430100, China +2
Neural network-driven domain decomposition for efficient solutions to the Helmholtz equation
Nov 19, 2025Victorita Dolean, Daria Hrebenshchykova, Stéphane Lanteri +1Neural PDE Solvers PDE Solving
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
Hard-constraint physics-residual networks for hydrogen crossover prediction and high-pressure extrapolation in PEM water electrolysis
Nov 8, 2025Yong-Woon Kim, Jihyeok Lee, Chulung Kang +1Neural Surrogate Modeling Physics-Informed ML
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
Physics-Informed Neural Networks for Speech Production
Nov 1, 2025Kazuya Yokota, Ryosuke Harakawa, Masaaki Baba +1Speech Processing Physics-Informed ML
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
LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries
Oct 29, 2025René P. Klausen, Ivan Timofeev, Jonas Naujoks +4Neural PDE Solvers PDE Solving
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
Complexity Dependent Error Rates for Physics-informed Statistical Learning via the Small-ball Method
Oct 27, 2025Diego MarcondesPhysics-Informed ML Statistical Learning Theory
Inverse Problem for Partial Differential Equations with Jump Discontinuities in Coefficients by Two-stage Physics-Informed Deep Learning and Statistical Mixture Models
Oct 16, 2025Zhikun Zhang, Guanyu Pan, Xiangjun Wang +2Bayesian Mixture Models Physics-Informed ML
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
Neural non-canonical Hamiltonian dynamics for long-time simulations
Oct 2, 2025Clémentine Courtès, Emmanuel Franck, Michael Kraus +2Dynamical Systems Nonlinear System Identification
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
MAD-PINN: A Decentralized Physics-Informed Machine Learning Framework for Safe and Optimal Multi-Agent Control
Sep 28, 2025Manan Tayal, Aditya Singh, Shishir Kolathaya +1Multi-Agent Control Constrained Optimization
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
Physics-informed GNN for medium-high voltage AC power flow with edge-aware attention and line search correction operator
Sep 26, 2025Changhun Kim, Timon Conrad, Redwanul Karim +6Efficient Neural Network Inference Graph Attention Networks
Pattern Recognition Lab, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany · Institute of Electrical Energy Systems, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
A Flow-rate-conserving CNN-based Domain Decomposition Method for Blood Flow Simulations
Sep 19, 2025Simon Klaes, Axel Klawonn, Natalie Kubicki +4PDE Solving PDE Surrogate Modeling
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
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
Data-driven multi-agent modelling of calcium interactions in cell culture: PINN vs Regularized Least-squares
May 23, 2025Aurora Poggi, Giuseppe Alessio D'Inverno, Hjalmar Brismar +3Nonlinear System Identification Parameter Estimation
KTH Royal Institute of Technology, Department of Mathematics, Stockholm, Sweden · International School for Advanced Studies (SISSA), Trieste, Italy · KTH Royal Institute of Technology, Department of Biophysics, Stockholm, Sweden +1
Repulsive Ensembles for Bayesian Inference in Physics-informed Neural Networks
May 22, 2025Philipp Pilar, Markus Heinonen, Niklas WahlströmUncertainty Quantification Physics-Informed ML
Department of Information Technology Uppsala University, Uppsala, Sweden · Department of Computer Science Aalto University, Espoo, Finland
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, 27100 Pavia, Italy · Department of Civil Engineering and Architecture, University of Pavia, 27100 Pavia, Italy · Institut Camille Jordan, Lyon 1 Université, 69622 Villeurbanne, France +1
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 +12Hyperspectral Imaging 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

Jan 28, 2026J/K move · Enter open · S save

Leveraging Differentiable PDE Solvers for Semi-Neural Spatial Reconstruction From Sparse Measurements

Ofek Aloni, Barak Fishbain

Department of Mathematics, Technion, Israel · Department of Civil and Environmental Engineering, Technion, Israel

Differentiable Physics Physics-Informed ML Computational Fluid Dynamics

Open paper AskPDF arXiv

Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications. State-of-the-art approaches to this problem either rely on spatial statistics that ignore the governing physics, integrate the physics into a multiple-objective optimization process, or require examples of the complete, fully-resolved simulation state during training, which are frequently unavailable outside of synthetic benchmarks. Here, we present a novel alternative that leverages recent advances in the integration of numerical simulators with data-driven models. Namely, we propose a hybrid modeling pipeline that couples Radial Basis Function (RBF) reconstruction with a Neural Network (NN) correction and a Partial Differential Equation (PDE) solver, so that the numerical simulator itself is embedded directly in the training loop of the learned component. Notably, the NN is trained without assuming availability of examples of the fully-resolved simulation state. This is made possible by implementing the PDE solver so that it is end-to-end differentiable, allowing gradients to be backpropagated through the simulation step during training. This grey-box methodology is evaluated on three standard benchmarks from fluid mechanics, where it achieves superior results over statistical and machine-learning-based reconstruction methods.