Error estimates for physics informed neural networks approximating the
Navier-Stokes equations

Error estimates for physics informed neural networks approximating the Navier-Stokes equations

17 March 2022

Ameya Dilip Jagtap

Papers citing "Error estimates for physics informed neural networks approximating the Navier-Stokes equations"

14 / 14 papers shown

Title
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-Aware Neural Implicit Solvers for multiscale, parametric PDEs with applications in heterogeneous media Matthaios Chatzopoulos P. Koutsourelakis AI4CE 39 3 0 29 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
Machine learning and domain decomposition methods -- a survey A. Klawonn M. Lanser J. Weber AI4CE 21 7 0 21 Dec 2023
Investigating the Ability of PINNs To Solve Burgers' PDE Near Finite-Time BlowUp Dibyakanti Kumar Anirbit Mukherjee 31 2 0 08 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
Error convergence and engineering-guided hyperparameter search of PINNs: towards optimized I-FENN performance Panos Pantidis Habiba Eldababy Christopher Miguel Tagle M. Mobasher 35 20 0 03 Mar 2023
How important are activation functions in regression and classification? A survey, performance comparison, and future directions Ameya Dilip Jagtap George Karniadakis AI4CE 31 71 0 06 Sep 2022
Error analysis for deep neural network approximations of parametric hyperbolic conservation laws Tim De Ryck Siddhartha Mishra PINN 13 10 0 15 Jul 2022
Is $L^2$ Physics-Informed Loss Always Suitable for Training Physics-Informed Neural Network? Chuwei Wang Shanda Li Di He Liwei Wang AI4CE PINN 23 28 0 04 Jun 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
Parallel Physics-Informed Neural Networks via Domain Decomposition K. Shukla Ameya Dilip Jagtap George Karniadakis PINN 101 274 0 20 Apr 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
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