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

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

3 April 2020

George Karniadakis

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

18 / 18 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
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 29 1 0 12 Jul 2023
Informed Learning by Wide Neural Networks: Convergence, Generalization and Sampling Complexity Jianyi Yang Shaolei Ren 32 3 0 02 Jul 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 23 201 0 23 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 16 139 0 14 Oct 2021
Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs Tim De Ryck Siddhartha Mishra PINN 21 100 0 28 Jun 2021
On the Representation of Solutions to Elliptic PDEs in Barron Spaces Ziang Chen Jianfeng Lu Yulong Lu 38 26 0 14 Jun 2021
A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equations N. R. Franco Andrea Manzoni P. Zunino 26 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 31 93 0 04 Jan 2021
Energy-based error bound of physics-informed neural network solutions in elasticity Mengwu Guo E. Haghighat PINN 51 28 0 18 Oct 2020
Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism L. McClenny U. Braga-Neto PINN 28 444 0 07 Sep 2020
When and why PINNs fail to train: A neural tangent kernel perspective Sizhuang He Xinling Yu P. Perdikaris 33 878 0 28 Jul 2020
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs Siddhartha Mishra Roberto Molinaro PINN 25 171 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 54 123 0 17 May 2020