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Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs

29 June 2020

Papers citing "Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs"

50 / 85 papers shown

Title
Operator Learning at Machine Precision Aras Bacho Aleksei G. Sorokin Xianjin Yang Théo Bourdais Edoardo Calvello Matthieu Darcy Alexander Hsu Bamdad Hosseini H. Owhadi 81 0 0 25 Nov 2025
Multi-robot Multi-source Localization in Complex Flows with Physics-Preserving Environment Models Benjamin D. Shaffer Victoria Edwards Brooks Kinch Nathaniel Trask M. A. Hsieh 92 0 0 17 Sep 2025
Physics-informed sensor coverage through structure preserving machine learning Benjamin D. Shaffer Brooks Kinch Joseph Klobusicky M. Ani Hsieh Nathaniel Trask AI4CE 117 1 0 12 Sep 2025
Theory Foundation of Physics-Enhanced Residual Learning Shixiao Liang Wang Chen Keke Long Peng Zhang Xiaopeng Li Jintao Ke AI4CE 100 0 0 30 Aug 2025
ViscoReg: Neural Signed Distance Functions via Viscosity Solutions Meenakshi Krishnan Ramani Duraiswami 149 0 0 01 Jul 2025
Acoustic Field Reconstruction in Tubes via Physics-Informed Neural Networks Xinmeng Luan Kazuya Yokota Gary Scavone AI4CE 124 4 0 18 May 2025
Solving Time-Fractional Partial Integro-Differential Equations Using Tensor Neural Network Zhongshuo Lin Qingkui Ma Hehu Xie Xiaobo Yin 220 3 0 02 Apr 2025
Physics-Informed Deep B-Spline Networks Zhuoyuan Wang Raffaele Romagnoli Jasmine Ratchford Yorie Nakahira PINN AI4CE 213 1 0 21 Mar 2025
Understanding Generalization in Physics Informed Models through Affine Variety Dimensions Takeshi Koshizuka Issei Sato AI4CE 458 1 0 31 Jan 2025
Physics-informed neural networks (PINNs) for numerical model error approximation and superresolution Bozhou Zhuang Sashank Rana Brandon Jones Danny Smyl PINN 208 0 0 14 Nov 2024
DeepSPoC: A Deep Learning-Based PDE Solver Governed by Sequential Propagation of Chaos Kai Du Yongle Xie Tao Zhou Yuancheng Zhou 115 0 0 29 Aug 2024
Parallel-in-Time Solutions with Random Projection Neural Networks M. Betcke L. Kreusser Davide Murari 116 2 0 19 Aug 2024
Physics-Informed Machine Learning for Grade Prediction in Froth FlotationMinerals Engineering (Miner. Eng.), 2024 Mahdi Nasiri Sahel Iqbal Simo Särkkä AI4CE 139 6 0 12 Aug 2024
Generalizable Physics-Informed Learning for Stochastic Safety-Critical Systems Zhuoyuan Wang Albert Chern Yorie Nakahira 335 1 0 11 Jul 2024
On the estimation rate of Bayesian PINN for inverse problems Yi Sun Debarghya Mukherjee Yves Atchadé PINN 244 1 0 21 Jun 2024
Two-level overlapping additive Schwarz preconditioner for training scientific machine learning applications Youngkyu Lee Alena Kopanicáková George Karniadakis AI4CE 211 3 0 16 Jun 2024
Error Analysis and Numerical Algorithm for PDE Approximation with Hidden-Layer Concatenated Physics Informed Neural Networks Yianxia Qian Yongchao Zhang Suchuan Dong PINN 161 0 0 10 Jun 2024
Astral: training physics-informed neural networks with error majorants V. Fanaskov Tianchi Yu Alexander Rudikov Ivan Oseledets 236 1 0 04 Jun 2024
Learning the Hodgkin-Huxley Model with Operator Learning Techniques Edoardo Centofanti Massimiliano Ghiotto Luca Franco Pavarino 121 10 0 04 Jun 2024
Loss Jump During Loss Switch in Solving PDEs with Neural NetworksCommunications in Computational Physics (Commun. Comput. Phys.), 2024 Zhiwei Wang Lulu Zhang Zhongwang Zhang Z. Xu 175 2 0 06 May 2024
BP-DeepONet: A new method for cuffless blood pressure estimation using the physcis-informed DeepONet Lingfeng Li Xue-Cheng Tai Raymond H. F. Chan 160 3 0 29 Feb 2024
Error Estimation for Physics-informed Neural Networks Approximating Semilinear Wave Equations Beatrice Lorenz Aras Bacho Gitta Kutyniok PINN 192 3 0 11 Feb 2024
Preconditioning for Physics-Informed Neural Networks Songming Liu Yan Yu J. Yao Zhongkai Hao Hang Su Youjia Wu Jun Zhu AI4CE PINN 185 7 0 01 Feb 2024
PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks Sizhuang He Bowen Li Yuhan Chen P. Perdikaris AI4CE PINN 483 78 0 01 Feb 2024
Physically Informed Synchronic-adaptive Learning for Industrial Systems Modeling in Heterogeneous Media with Unavailable Time-varying InterfaceIEEE Transactions on Automation Science and Engineering (T-ASE), 2024 Aina Wang Pan Qin Xi-Ming Sun PINN AI4CE 89 0 0 26 Jan 2024
Separable Physics-Informed Neural Networks for the solution of elasticity problems V. A. Es'kin Danil V. Davydov Julia V. Guréva Alexey O. Malkhanov Mikhail E. Smorkalov PINN AI4CE 247 5 0 24 Jan 2024
Robust Physics Informed Neural Networks Marcin Lo's Maciej Paszyñski PINN 204 0 0 04 Jan 2024
Physics-informed Neural Network Estimation of Material Properties in Soft Tissue Nonlinear Biomechanical ModelsComputational Mechanics (CM), 2023 Federica Caforio Francesco Regazzoni S. Pagani Elias Karabelas Christoph M. Augustin Gundolf Haase Gernot Plank A. Quarteroni PINN 237 34 0 15 Dec 2023
Physics-Informed Deep Learning of Rate-and-State Fault FrictionComputer Methods in Applied Mechanics and Engineering (CMAME), 2023 Cody Rucker Brittany A. Erickson PINN AI4CE 203 14 0 14 Dec 2023
Data-driven localized waves and parameter discovery in the massive Thirring model via extended physics-informed neural networks with interface zones Christian Berger Sadok Ben Toumia Zijian Zhou Zhenya Yan PINN 155 14 0 29 Sep 2023
Approximating High-Dimensional Minimal Surfaces with Physics-Informed Neural Networks Steven Zhou Xiaojing Ye PINN 178 0 0 05 Sep 2023
Bayesian Reasoning for Physics Informed Neural Networks K. Graczyk Kornel Witkowski 212 0 0 25 Aug 2023
On the accuracy of interpolation based on single-layer artificial neural networks with a focus on defeating the Runge phenomenonSoft Computing - A Fusion of Foundations, Methodologies and Applications (Soft Comput.), 2023 F. Auricchio Maria Roberta Belardo Gianluca Fabiani Francesco Calabrò A. Pascaner 202 2 0 21 Aug 2023
Neural oscillators for generalization of physics-informed machine learningAAAI Conference on Artificial Intelligence (AAAI), 2023 Taniya Kapoor Abhishek Chandra D. Tartakovsky Hongrui Wang Alfredo Núñez R. Dollevoet AI4CE 205 16 0 17 Aug 2023
Physics-Informed Deep Learning to Reduce the Bias in Joint Prediction of Nitrogen Oxides Lianfa Li Roxana Khalili F. Lurmann N. Pavlovic Jun Wu ... M. Franklin T. Bastain S. Farzan C. Breton R. Habre AI4CE 123 6 0 14 Aug 2023
Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNsJournal of Fluid Mechanics (JFM), 2023 Elham Kiyani M. Kooshkbaghi K. Shukla R. Koneru Zhen Li L. Bravo A. Ghoshal George Karniadakis M. Karttunen AI4CE 169 7 0 18 Jul 2023
Auxiliary-Tasks Learning for Physics-Informed Neural Network-Based Partial Differential Equations Solving Junjun Yan Xinhai Chen Zhichao Wang Enqiang Zhou Jie Liu PINN AI4CE 230 1 0 12 Jul 2023
A Deep Learning Framework for Solving Hyperbolic Partial Differential Equations: Part I Rajat Arora PINN AI4CE 142 1 0 09 Jul 2023
Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategiesSIAM Journal on Scientific Computing (SISC), 2023 Alena Kopanicáková Hardik Kothari George Karniadakis Rolf Krause AI4CE 197 25 0 30 Jun 2023
ST-PINN: A Self-Training Physics-Informed Neural Network for Partial Differential EquationsIEEE International Joint Conference on Neural Network (IJCNN), 2023 Junjun Yan Xinhai Chen Zhichao Wang Enqiang Zhoui Jie Liu PINN DiffM AI4CE 158 16 0 15 Jun 2023
A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural NetworksComputational optimization and applications (Comput. Optim. Appl.), 2023 Serge Gratton Valentin Mercier E. Riccietti P. Toint AI4CE 187 11 0 23 May 2023
A Survey on Solving and Discovering Differential Equations Using Deep Neural Networks Hyeonjung Jung Jung Jayant Gupta B. Jayaprakash Matthew J. Eagon Harish Selvam Carl Molnar W. Northrop Shashi Shekhar AI4CE 241 7 0 26 Apr 2023
Maximum-likelihood Estimators in Physics-Informed Neural Networks for High-dimensional Inverse ProblemsComputers and Chemical Engineering (Comput. Chem. Eng.), 2023 G. S. Gusmão A. Medford PINN 141 12 0 12 Apr 2023
Error Analysis of Physics-Informed Neural Networks for Approximating Dynamic PDEs of Second Order in Time Y. Qian Yongchao Zhang Yuanfei Huang S. Dong PINN 189 3 0 22 Mar 2023
On the uncertainty analysis of the data-enabled physics-informed neural network for solving neutron diffusion eigenvalue problemNuclear science and engineering (NSE), 2023 Yu Yang Helin Gong Qihong Yang Yangtao Deng Qiaolin He Shiquan Zhang DiffM 190 13 0 15 Mar 2023
Error convergence and engineering-guided hyperparameter search of PINNs: towards optimized I-FENN performanceSocial Science Research Network (SSRN), 2023 Panos Pantidis Habiba Eldababy Christopher Miguel Tagle M. Mobasher 211 26 0 03 Mar 2023
A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositionsJournal of Computational Physics (JCP), 2023 Michael Penwarden Ameya Dilip Jagtap Shandian Zhe George Karniadakis Robert M. Kirby PINN AI4CE 230 83 0 28 Feb 2023
h-analysis and data-parallel physics-informed neural networksScientific Reports (Sci Rep), 2023 Paul Escapil-Inchauspé G. A. Ruz PINN AI4CE 202 5 0 17 Feb 2023
On the Generalization of PINNs outside the training domain and the Hyperparameters influencing it Andrea Bonfanti Roberto Santana M. Ellero Babak Gholami AI4CE PINN 251 15 0 15 Feb 2023
Can Physics-Informed Neural Networks beat the Finite Element Method?IMA Journal of Applied Mathematics (IMA J. Appl. Math.), 2023 T. G. Grossmann Urszula Julia Komorowska J. Latz Carola-Bibiane Schönlieb PINN AI4CE 247 150 0 08 Feb 2023