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.

Parameterized Temporal Extrapolation of PDEs via Disentangled Latent Dynamics Manifold Fusion
Mar 13, 2026Zhangyong Liang, Jihong Zhu, Huanhuan GaoLatent Dynamics Modeling PDE Solving
National Center for Applied Mathematics, Tianjin University, Tianjin, 300072, PR China · School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, 710072, China · School of Mechanical and Aerospace Engineering, Jilin University, Changchun, 130025, China
Scaling Laws and Pathologies of Single-Layer PINNs: Network Width and PDE Nonlinearity
Mar 13, 2026Faris ChaudhryPhysics-Informed ML Neural Scaling Laws
Department of Computer Science, Imperial College London
Bridging the Visual-to-Physical Gap: Physically Aligned Representations for Fall Risk Analysis
Mar 12, 2026Xianqi ZhangMotion Representation Learning Clinical Risk Prediction
Faculty of Computing, Harbin Institute of Technology, Harbin 150001, China · Suzhou Research Institute, Harbin Institute of Technology, Suzhou 215104, China
UniPINN: A Unified PINN Framework for Multi-task Learning of Diverse Navier-Stokes Equations
Mar 11, 2026Dengdi Sun, Jie Chen, Xiao Wang +1Physics-Informed ML Multi-Task Learning
Key Laboratory of Intelligent Computing & Signal Processing (ICSP), Ministry of Education, School of Artificial Intelligence, Anhui University, Hefei 230601, China · Anhui Provincial Key Laboratory of Multimodal Cognitive Computing, School of Computer Science and Technology, Anhui University, Hefei 230601, China
Task Aware Modulation Using Representation Learning for Upsaling of Terrestrial Carbon Fluxes
Mar 10, 2026Aleksei Rozanov, Arvind Renganathan, Vipin KumarClimate Science Physics-Informed ML
University of Minnesota, Twin Cities
Flow Field Reconstruction via Voronoi-Enhanced Physics-Informed Neural Networks with End-to-End Sensor Placement Optimization
Mar 10, 2026Renjie Xiao, Bingteng Sun, Yiling Chen +3Computational Fluid Dynamics Physics-Informed ML
Advanced Gas Turbine Laboratory, Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing, 100190, China · National Key Laboratory of Science and Technology on Advanced Light-duty Gas-turbine, Beijing, 100190, China · School of Computer Science and Technology Shandong University Qingdao Shandong 266237 China +3
Evidential Perfusion Physics-Informed Neural Networks with Residual Uncertainty Quantification
Mar 10, 2026Junhyeok Lee, Minseo Choi, Han Jang +5Evidential Deep Learning Uncertainty Quantification
Cancer Biology, Seoul National University College of Medicine, Seoul, Korea · Radiology, Seoul National University Hospital, Seoul, Korea · Bioengineering, Seoul National University, Seoul, Korea +3
Two Teachers Better Than One: Hardware-Physics Co-Guided Distributed Scientific Machine Learning
Mar 10, 2026Yuchen Yuan, Junhuan Yang, Hao Wan +4Scientific ML Edge ML
George Mason University, Fairfax, VA, USA · University of North Carolina at Chapel Hill, NC, USA
MUSA-PINN: Multi-scale Weak-form Physics-Informed Neural Networks for Fluid Flow in Complex Geometries
Mar 9, 2026Weizheng Zhang, Xunjie Xie, Hao Pan +4Neural PDE Solvers PDE Solving
Shandong University, Qingdao, China · Tsinghua University, Beijing, China · Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing, China
PSTNet: Physically-Structured Turbulence Network
Mar 9, 2026Boris Kriuk, Fedor KriukPhysics-Informed ML
Faculty of Engineering & Information Technology, University of Technology Sydney, Sydney, New South Wales, Australia
Learning embeddings of non-linear PDEs: the Burgers' equation
Mar 8, 2026Pedro Tarancón-Álvarez, Leonid Sarieddine, Pavlos Protopapas +1Physics-Informed ML PDE Solving
Departament de F´ısica Qu´antica i Astrof´ısica, Universitat de Barcelona Institut de Ciencies del Cosmos (ICC), Universitat de Barcelona, Marti i Franques 1, ES-08028, Barcelona, Spain. · Institute for Applied Computational Science Harvard University Cambridge, MA, USA · Institut de Ciencies del Cosmos (ICC), Universitat de Barcelona, Marti i Franques 1, ES-08028, Barcelona, Spain. +1
Inverse Resistive Force Theory (I-RFT): Learning granular properties through robot-terrain physical interactions
Mar 8, 2026Shipeng Liu, Feng Xue, Yifeng Zhang +2Terrain-Aware Robot Locomotion Granular Terrain Locomotion
University of Southern California, Los Angeles, CA 90089, USA
Partial Differential Equations in the Age of Machine Learning: A Critical Synthesis of Classical, Machine Learning, and Hybrid Methods
Mar 8, 2026Mohammad Nooraiepour, Jakub Wiktor Both, Teeratorn Kadeethum +1PDE Solving Partial Differential Equations
Faculty of Mathematics and Natural Sciences, University of Oslo, 1047 Blindern, 0316 Oslo, Norway · Department of Mathematics, University of Bergen, Bergen, Norway · AI Lab, Siemens Energy, Orlando, FL 32826, USA +1
Joint 3D Gravity and Magnetic Inversion via Rectified Flow and Ginzburg-Landau Guidance
Mar 6, 2026Dhruman Gupta, Yashas Shende, Aritra Das +2Physics-Informed ML Inverse Problems
Ashoka University
Prediction of Steady-State Flow through Porous Media Using Machine Learning Models
Mar 6, 2026Jinhong Wang, Matei C. Ignuta-Ciuncanu, Ricardo F. Martinez-Botas +1Porous Media Flow PDE Surrogate Modeling
Department of Mechanical Engineering, Imperial College London, South Kensington Campus, London, SW7 2AZ, , United Kingdom
Diversity-Aware Adaptive Collocation for Physics-Informed Neural Networks via Sparse QUBO Optimization and Hybrid Coresets
Mar 6, 2026Hadi Salloum, Maximilian Mifsud Bonici, Sinan Ibrahim +2Physics-Informed ML Coreset Selection
Research Center for Artificial Intelligence, Innopolis University, Innopolis, Russia · Moscow Center for Advanced Studies, 20, Kulakova Str., Moscow, Russia · Laboratory of Quantum Computing, Innopolis University, Innopolis, Russia +5
Learning Where the Physics Is: Probabilistic Adaptive Sampling for Stiff PDEs
Mar 6, 2026Akshay Govind Srinivasan, Balaji SrinivasanNeural PDE Solvers PDE Solving
Indian Institute of Technology, Madras Chennai, TN 600107, India
SPyCer: Semi-Supervised Physics-Guided Contextual Attention for Near-Surface Air Temperature Estimation from Satellite Imagery
Mar 5, 2026Sofiane Bouaziz, Adel Hafiane, Raphael Canals +1Remote Sensing Physics-Informed ML
INSA CVL, Université d’Orléans, PRISME UR 4229, Bourges, 18022, Centre Val de Loire, France · Université d’Orléans, INSA CVL, PRISME UR 4229, Orléans, 45067, Centre Val de Loire, France · Université d’Orléans, CEDETE, UR 1210, Orléans, 45067, Centre Val de Loire, France
Improving the accuracy of physics-informed neural networks via last-layer retraining
Mar 4, 2026Saad Qadeer, Panos StinisNeural PDE Solvers Physics-Informed ML
Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, Richland, WA
LUMINA: Foundation Models for Topology Transferable ACOPF
Mar 4, 2026Yijiang Li, Zeeshan Memon, Hongwei Jin +7Physical Foundation Models Scientific ML
Argonne National Laboratory, Lemont, IL 60439, USA · Emory University, Atlanta, GA 30322, USA · Sogang University, Seoul, South Korea
Non-Invasive Reconstruction of Cardiac Activation Dynamics Using Physics-Informed Neural Networks
Mar 4, 2026Nathan Dermul, Hans DierckxPhysics-Informed ML
Department of Cardiovascular Sciences, Cardiovascular Imaging and Dynamics, KU Leuven, Belgium. · Department of Cardiology, Leiden University Medical Centre, Albinusdreef 2, Leiden, 2333 ZA, the Netherlands. · Mathematical Institute, Leiden University, Einsteinweg 55, Leiden, 2333 CC, the Netherlands. +1
Physics-informed post-processing of stabilized finite element solutions for transient convection-dominated problems
Mar 3, 2026Süleyman Cengizci, Ömür Uğur, Srinivasan NatesanPDE Solving Physics-Informed ML
Department of Computer Technologies, Antalya Bilim University, Antalya 07190, Turkey · Institute of Applied Mathematics, Middle East Technical University, Ankara 06800, Turkey · Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati 781039, India
Stabilized Adaptive Loss and Residual-Based Collocation for Physics-Informed Neural Networks
Mar 3, 2026Divyavardhan Singh, Shubham Kamble, Dimple Sonone +1Physics-Informed ML PDE Solving
Sardar Vallabhbhai National Institute of Technology (SVNIT), Surat, India
Enhancing Physics-Informed Neural Networks with Domain-aware Fourier Features: Towards Improved Performance and Interpretable Results
Mar 3, 2026Alberto Miño Calero, Luis Salamanca, Konstantinos E. TatsisFourier Feature Embeddings Neural Network Interpretability
Department of Engineering Cybernetics NTNU, Trondheim, Norway · Swiss Data Science Center (SDSC) ETH Zürich, Zürich, Switzerland
Neural Electromagnetic Fields for High-Resolution Material Parameter Reconstruction
Mar 3, 2026Zhe Chen, Peilin Zheng, Wenshuo Chen +3Materials Property Prediction Inverse Problems
Xidian University · The Hong Kong University of Science and Technology
Solving Inverse PDE Problems using Minimization Methods and AI
Mar 2, 2026Noura Al Helwani, Sophie Moufawad, Georges SakrPDE Solving PDE Inverse Problems
Department of Physics, American University of Beirut, Lebanon · Department of Mathematics, American University of Beirut, Lebanon · The authors would like to acknowledge
Operator Learning Using Weak Supervision from Walk-on-Spheres
Mar 1, 2026Hrishikesh Viswanath, Hong Chul Nam, Xi Deng +3PDE Operator Learning Physics-Informed ML
Purdue University, USA · ETH Zurich, Switzerland · California Institute of Technology, USA +1
Data-Free Finite-Volume Convolutional Neural Networks for Steady Compressible Euler Flow around a Circular Cylinder
Mar 1, 2026Ryosuke YanoNeural PDE Solvers Physics-Informed ML
Tokio Marine dR Co., Ltd., 1-5-1, Otemachi, Chiyoda-ku, Tokyo, 100-0004, Japan.
Learning to Weigh Waste: A Physics-Informed Multimodal Fusion Framework and Large-Scale Dataset for Commercial and Industrial Applications
Mar 1, 2026Md. Adnanul Islam, Wasimul Karim, Md Mahbub Alam +7Multimodal Fusion Physics-Informed ML
Department of Computer Science and Engineering, United International University, Dhaka 1212, Bangladesh and also with Applied Artificial INtelligence and Intelligent Systems (AAIINS) Laboratory, Dhaka 1217, Bangladesh · Department of Data Science and Artificial Intelligence, Monash University, 3800, Melbourne, Australia, and also with Applied Artificial INtelligence and Intelligent Systems (AAIINS) Laboratory, Dhaka 1217, Bangladesh · Faculty of Science and Technology, Charles Darwin University, Darwin, NT 0810, Australia +1
Robust Parameter and State Estimation in Multiscale Neuronal Systems Using Physics-Informed Neural Networks
Feb 27, 2026Changliang Wei, Yangyang Wang, Xueyu ZhuParameter Estimation Physics-Informed ML
Department of Mathematics, University of Iowa, Iowa City, IA 52246, USA. · Department of Mathematics, Volen National Center for Complex Systems, Brandeis University, Waltham, MA 02453, USA.

Mar 13, 2026J/K move · Enter open · S save

Parameterized Temporal Extrapolation of PDEs via Disentangled Latent Dynamics Manifold Fusion

Zhangyong Liang, Jihong Zhu, Huanhuan Gao

National Center for Applied Mathematics, Tianjin University, Tianjin, 300072, PR China · School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, 710072, China · School of Mechanical and Aerospace Engineering, Jilin University, Changchun, 130025, China

Latent Dynamics Modeling PDE Solving PDE Surrogate Modeling Physics-Informed ML

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Generalizing neural surrogate models across different PDE parameters remains difficult because changes in PDE coefficients often make learning harder and optimization less stable. The problem becomes even more severe when the model must also predict beyond the training time range. Existing methods usually cannot handle parameter generalization and temporal extrapolation at the same time. Standard parameterized models treat time as just another input and therefore fail to capture intrinsic dynamics, while recent continuous-time latent methods often rely on expensive test-time auto-decoding for each instance, which is inefficient and can disrupt continuity across the parameterized solution space. To address this, we propose Disentangled Latent Dynamics Manifold Fusion (DLDMF), a physics-informed framework that explicitly separates space, time, and parameters. Instead of unstable auto-decoding, DLDMF maps PDE parameters directly to a continuous latent embedding through a feed-forward network. This embedding initializes and conditions a latent state whose evolution is governed by a parameter-conditioned Neural ODE. We further introduce a dynamic manifold fusion mechanism that uses a shared decoder to combine spatial coordinates, parameter embeddings, and time-evolving latent states to reconstruct the corresponding spatiotemporal solution. By modeling prediction as latent dynamic evolution rather than static coordinate fitting, DLDMF reduces interference between parameter variation and temporal evolution while preserving a smooth and coherent solution manifold. As a result, it performs well on unseen parameter settings and in long-term temporal extrapolation. Experiments on several benchmark problems show that DLDMF consistently outperforms state-of-the-art baselines in accuracy, parameter generalization, and extrapolation robustness.