On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs

3 April 2020

Papers citing "On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs"

37 / 37 papers shown

Title
Label Propagation Training Schemes for Physics-Informed Neural Networks and Gaussian Processes Ming Zhong Dehao Liu Raymundo Arroyave U. Braga-Neto AI4CE SSL 26 1 0 08 Apr 2024
Approximation of Solution Operators for High-dimensional PDEs Nathan Gaby Xiaojing Ye 30 0 0 18 Jan 2024
Moving Sampling Physics-informed Neural Networks induced by Moving Mesh PDE Yu Yang Qihong Yang Yangtao Deng Qiaolin He 16 3 0 14 Nov 2023
Neural oscillators for generalization of physics-informed machine learning Taniya Kapoor Abhishek Chandra D. Tartakovsky Hongrui Wang Alfredo Núñez R. Dollevoet AI4CE 32 11 0 17 Aug 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 31 1 0 12 Jul 2023
ST-PINN: A Self-Training Physics-Informed Neural Network for Partial Differential Equations Junjun Yan Xinhai Chen Zhichao Wang Enqiang Zhoui Jie Liu PINN DiffM AI4CE 32 10 0 15 Jun 2023
Convergence Analysis of the Deep Galerkin Method for Weak Solutions Yuling Jiao Yanming Lai Yang Wang Haizhao Yang Yunfei Yang 26 3 0 05 Feb 2023
Neural Control of Parametric Solutions for High-dimensional Evolution PDEs Nathan Gaby X. Ye Haomin Zhou 19 6 0 31 Jan 2023
Physics-Informed Neural Network Method for Parabolic Differential Equations with Sharply Perturbed Initial Conditions Yifei Zong Qizhi He A. Tartakovsky PINN 22 18 0 18 Aug 2022
wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation laws Tim De Ryck Siddhartha Mishra Roberto Molinaro PINN 40 29 0 18 Jul 2022
Informed Learning by Wide Neural Networks: Convergence, Generalization and Sampling Complexity Jianyi Yang Shaolei Ren 35 3 0 02 Jul 2022
Generic bounds on the approximation error for physics-informed (and) operator learning Tim De Ryck Siddhartha Mishra PINN 63 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 49 115 0 17 Mar 2022
Physics-informed neural networks for inverse problems in supersonic flows Ameya Dilip Jagtap Zhiping Mao Nikolaus Adams George Karniadakis PINN 26 201 0 23 Feb 2022
Learning Physics-Informed Neural Networks without Stacked Back-propagation Di He Shanda Li Wen-Wu Shi Xiaotian Gao Jia Zhang Jiang Bian Liwei Wang Tie-Yan Liu DiffM PINN AI4CE 18 23 0 18 Feb 2022
State-of-the-Art Review of Design of Experiments for Physics-Informed Deep Learning Sourav Das S. Tesfamariam PINN AI4CE 26 19 0 13 Feb 2022
Solving time dependent Fokker-Planck equations via temporal normalizing flow Xiaodong Feng Li Zeng Tao Zhou AI4CE 36 25 0 28 Dec 2021
Physics informed neural networks for continuum micromechanics Alexander Henkes Henning Wessels R. Mahnken PINN AI4CE 32 139 0 14 Oct 2021
Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs Tim De Ryck Siddhartha Mishra PINN 26 100 0 28 Jun 2021
On the Representation of Solutions to Elliptic PDEs in Barron Spaces Ziang Chen Jianfeng Lu Yulong Lu 38 27 0 14 Jun 2021
Accelerating Dynamical System Simulations with Contracting and Physics-Projected Neural-Newton Solvers Samuel C. Chevalier Jochen Stiasny Spyros Chatzivasileiadis 33 3 0 04 Jun 2021
Physics Informed Convex Artificial Neural Networks (PICANNs) for Optimal Transport based Density Estimation Amanpreet Singh Martin Bauer S. Joshi OT 6 1 0 02 Apr 2021
Physics-informed neural networks for the shallow-water equations on the sphere Alexander Bihlo R. Popovych 14 77 0 01 Apr 2021
Solving and Learning Nonlinear PDEs with Gaussian Processes Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 34 153 0 24 Mar 2021
A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equations N. R. Franco Andrea Manzoni P. Zunino 33 45 0 10 Mar 2021
Reproducing Activation Function for Deep Learning Senwei Liang Liyao Lyu Chunmei Wang Haizhao Yang 36 21 0 13 Jan 2021
Hybrid FEM-NN models: Combining artificial neural networks with the finite element method Sebastian K. Mitusch S. Funke M. Kuchta AI4CE 44 94 0 04 Jan 2021
$NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework$ NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework O. Hennigh S. Narasimhan M. A. Nabian Akshay Subramaniam Kaustubh Tangsali M. Rietmann J. Ferrandis Wonmin Byeon Z. Fang S. Choudhry PINN AI4CE 93 126 0 14 Dec 2020
Energy-based error bound of physics-informed neural network solutions in elasticity Mengwu Guo E. Haghighat PINN 56 28 0 18 Oct 2020
Large-scale Neural Solvers for Partial Differential Equations Patrick Stiller Friedrich Bethke M. Böhme R. Pausch Sunna Torge A. Debus J. Vorberger Michael Bussmann Nico Hoffmann AI4CE 16 26 0 08 Sep 2020
Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism L. McClenny U. Braga-Neto PINN 28 446 0 07 Sep 2020
When and why PINNs fail to train: A neural tangent kernel perspective Sizhuang He Xinling Yu P. Perdikaris 33 881 0 28 Jul 2020
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs Siddhartha Mishra Roberto Molinaro PINN 16 262 0 29 Jun 2020
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs Siddhartha Mishra Roberto Molinaro PINN 30 171 0 29 Jun 2020
DiscretizationNet: A Machine-Learning based solver for Navier-Stokes Equations using Finite Volume Discretization Rishikesh Ranade C. Hill Jay Pathak AI4CE 59 123 0 17 May 2020
Model Reduction and Neural Networks for Parametric PDEs K. Bhattacharya Bamdad Hosseini Nikola B. Kovachki Andrew M. Stuart 24 319 0 07 May 2020
hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition E. Kharazmi Zhongqiang Zhang George Karniadakis 135 510 0 11 Mar 2020