Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs

28 June 2021

Papers citing "Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs"

41 / 41 papers shown

Title
Improved Uncertainty Quantification in Physics-Informed Neural Networks Using Error Bounds and Solution Bundles P. Flores Olga Graf P. Protopapas K. Pichara PINN 33 0 0 09 May 2025
Physics-Informed Deep B-Spline Networks for Dynamical Systems Zhuoyuan Wang Raffaele Romagnoli Jasmine Ratchford Yorie Nakahira PINN AI4CE 53 0 0 21 Mar 2025
Challenges and Advancements in Modeling Shock Fronts with Physics-Informed Neural Networks: A Review and Benchmarking Study J. Abbasi Ameya D. Jagtap Ben Moseley Aksel Hiorth P. Andersen PINN AI4CE 44 1 0 14 Mar 2025
Understanding Generalization in Physics Informed Models through Affine Variety Dimensions Takeshi Koshizuka Issei Sato AI4CE 109 0 0 31 Jan 2025
Exact and approximate error bounds for physics-informed neural networks Augusto T. Chantada Pavlos Protopapas Luca Gomez Bachar Susana J. Landau Claudia G. Scóccola PINN 59 0 0 21 Nov 2024
Beyond Derivative Pathology of PINNs: Variable Splitting Strategy with Convergence Analysis Yesom Park Changhoon Song Myungjoo Kang 28 2 0 30 Sep 2024
Parallel-in-Time Solutions with Random Projection Neural Networks M. Betcke L. Kreusser Davide Murari 26 1 0 19 Aug 2024
Generalizable Physics-Informed Learning for Stochastic Safety-Critical Systems Zhuoyuan Wang Albert Chern Yorie Nakahira 27 0 0 11 Jul 2024
Feynman-Kac Operator Expectation Estimator Jingyuan Li Wei Liu 30 0 0 02 Jul 2024
Solving Poisson Equations using Neural Walk-on-Spheres Hong Chul Nam Julius Berner Anima Anandkumar 34 3 0 05 Jun 2024
Astral: training physics-informed neural networks with error majorants V. Fanaskov Tianchi Yu Alexander Rudikov Ivan V. Oseledets 33 1 0 04 Jun 2024
Physics-informed deep learning and compressive collocation for high-dimensional diffusion-reaction equations: practical existence theory and numerics Simone Brugiapaglia N. Dexter Samir Karam Weiqi Wang AI4CE DiffM 43 1 0 03 Jun 2024
Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations Chuqi Chen Yahong Yang Yang Xiang Wenrui Hao 26 2 0 23 May 2024
Unveiling the optimization process of Physics Informed Neural Networks: How accurate and competitive can PINNs be? Jorge F. Urbán P. Stefanou José A. Pons PINN 45 6 0 07 May 2024
Deep adaptive sampling for surrogate modeling without labeled data Xili Wang Keju Tang Jiayu Zhai Xiaoliang Wan Chao Yang 35 2 0 17 Feb 2024
Correctness Verification of Neural Networks Approximating Differential Equations Petros Ellinas Rahul Nellikkath Ignasi Ventura Jochen Stiasny Spyros Chatzivasileiadis 37 1 0 12 Feb 2024
Error Estimation for Physics-informed Neural Networks Approximating Semilinear Wave Equations Beatrice Lorenz Aras Bacho Gitta Kutyniok PINN 16 2 0 11 Feb 2024
Preconditioning for Physics-Informed Neural Networks Songming Liu Chang Su J. Yao Zhongkai Hao Hang Su Youjia Wu Jun Zhu AI4CE PINN 38 5 0 01 Feb 2024
Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss Yahong Yang Juncai He AI4CE 32 7 0 31 Jan 2024
Binary structured physics-informed neural networks for solving equations with rapidly changing solutions Yanzhi Liu Ruifan Wu Ying Jiang PINN 21 2 0 23 Jan 2024
Optimal Deep Neural Network Approximation for Korobov Functions with respect to Sobolev Norms Yahong Yang Yulong Lu 37 3 0 08 Nov 2023
An operator preconditioning perspective on training in physics-informed machine learning Tim De Ryck Florent Bonnet Siddhartha Mishra Emmanuel de Bezenac AI4CE 39 14 0 09 Oct 2023
$A numerical approach for the fractional Laplacian via deep neural networks$ A numerical approach for the fractional Laplacian via deep neural networks Nicolás Valenzuela 29 3 0 30 Aug 2023
MultiAdam: Parameter-wise Scale-invariant Optimizer for Multiscale Training of Physics-informed Neural Networks J. Yao Chang Su Zhongkai Hao Songming Liu Hang Su Jun Zhu ODL PINN AI4CE 11 12 0 05 Jun 2023
Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs Pau Batlle Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 34 17 0 08 May 2023
Convergence and error analysis of PINNs Nathan Doumèche Gérard Biau D. Boyer PINN AI4CE 42 17 0 02 May 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 35 3 0 15 Feb 2023
Entropy-dissipation Informed Neural Network for McKean-Vlasov Type PDEs Zebang Shen Zhenfu Wang 19 4 0 11 Feb 2023
Neural tangent kernel analysis of PINN for advection-diffusion equation M. Saadat B. Gjorgiev L. Das G. Sansavini 25 0 0 21 Nov 2022
Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology Zheyuan Hu Ameya Dilip Jagtap George Karniadakis Kenji Kawaguchi 31 75 0 16 Nov 2022
Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications Zhongkai Hao Songming Liu Yichi Zhang Chengyang Ying Yao Feng Hang Su Jun Zhu PINN AI4CE 28 89 0 15 Nov 2022
wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation laws Tim De Ryck Siddhartha Mishra Roberto Molinaro PINN 27 28 0 18 Jul 2022
Evaluating Error Bound for Physics-Informed Neural Networks on Linear Dynamical Systems Shuheng Liu Xiyue Huang P. Protopapas PINN 13 5 0 03 Jul 2022
Generic bounds on the approximation error for physics-informed (and) operator learning Tim De Ryck Siddhartha Mishra PINN 59 59 0 23 May 2022
Error estimates for physics informed neural networks approximating the Navier-Stokes equations Tim De Ryck Ameya Dilip Jagtap S. Mishra PINN 40 115 0 17 Mar 2022
Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next S. Cuomo Vincenzo Schiano Di Cola F. Giampaolo G. Rozza Maizar Raissi F. Piccialli PINN 26 1,179 0 14 Jan 2022
Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems Nikolas Nusken Lorenz Richter PINN DiffM 31 27 0 07 Dec 2021
When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization? Zheyuan Hu Ameya Dilip Jagtap George Karniadakis Kenji Kawaguchi AI4CE PINN 22 83 0 20 Sep 2021
Fourier Neural Operator for Parametric Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 211 2,287 0 18 Oct 2020
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs Siddhartha Mishra Roberto Molinaro PINN 25 170 0 29 Jun 2020
B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data Liu Yang Xuhui Meng George Karniadakis PINN 183 759 0 13 Mar 2020