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"

26 / 26 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
Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs Elham Kiyani M. Kooshkbaghi K. Shukla R. Koneru Zhen Li L. Bravo A. Ghoshal George Karniadakis M. Karttunen AI4CE 37 4 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 26 1 0 12 Jul 2023
A Deep Learning Framework for Solving Hyperbolic Partial Differential Equations: Part I Rajat Arora PINN AI4CE 22 1 0 09 Jul 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 35 5 0 26 Apr 2023
Error convergence and engineering-guided hyperparameter search of PINNs: towards optimized I-FENN performance Panos Pantidis Habiba Eldababy Christopher Miguel Tagle M. Mobasher 29 20 0 03 Mar 2023
h-analysis and data-parallel physics-informed neural networks Paul Escapil-Inchauspé G. A. Ruz PINN AI4CE 27 2 0 17 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
Physics-informed neural networks for operator equations with stochastic data Paul Escapil-Inchauspé G. A. Ruz 26 2 0 15 Nov 2022
Partial Differential Equations Meet Deep Neural Networks: A Survey Shudong Huang Wentao Feng Chenwei Tang Jiancheng Lv AI4CE AIMat 24 17 0 27 Oct 2022
A Dimension-Augmented Physics-Informed Neural Network (DaPINN) with High Level Accuracy and Efficiency Weilong Guan Kai-Ping Yang Yinsheng Chen Zhong Guan PINN AI4CE 18 12 0 19 Oct 2022
Physics-Informed Neural Networks for Shell Structures Jan-Hendrik Bastek D. Kochmann AI4CE 14 51 0 26 Jul 2022
Revisiting PINNs: Generative Adversarial Physics-informed Neural Networks and Point-weighting Method Wensheng Li Chao Zhang Chuncheng Wang Hanting Guan Dacheng Tao DiffM PINN 14 12 0 18 May 2022
Self-scalable Tanh (Stan): Faster Convergence and Better Generalization in Physics-informed Neural Networks Raghav Gnanasambandam Bo Shen Jihoon Chung Xubo Yue Zhenyu Zhen Kong LRM 32 12 0 26 Apr 2022
Error estimates for physics informed neural networks approximating the Navier-Stokes equations Tim De Ryck Ameya Dilip Jagtap S. Mishra PINN 27 115 0 17 Mar 2022
Physics-informed neural networks for inverse problems in supersonic flows Ameya Dilip Jagtap Zhiping Mao Nikolaus Adams George Karniadakis PINN 18 201 0 23 Feb 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
Improved architectures and training algorithms for deep operator networks Sifan Wang Hanwen Wang P. Perdikaris AI4CE 49 105 0 04 Oct 2021
NeuFENet: Neural Finite Element Solutions with Theoretical Bounds for Parametric PDEs Biswajit Khara Aditya Balu Ameya Joshi S. Sarkar C. Hegde A. Krishnamurthy Baskar Ganapathysubramanian 24 19 0 04 Oct 2021
An artificial neural network approach to bifurcating phenomena in computational fluid dynamics F. Pichi F. Ballarin G. Rozza J. Hesthaven AI4CE 20 71 0 22 Sep 2021
Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networks Yihang Gao Michael K. Ng 35 28 0 30 Aug 2021
Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs Tim De Ryck Siddhartha Mishra PINN 11 100 0 28 Jun 2021
A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue Problems Jianfeng Lu Yulong Lu 31 29 0 04 May 2021
A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equations N. R. Franco Andrea Manzoni P. Zunino 18 45 0 10 Mar 2021
An overview on deep learning-based approximation methods for partial differential equations C. Beck Martin Hutzenthaler Arnulf Jentzen Benno Kuckuck 30 146 0 22 Dec 2020
B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data Liu Yang Xuhui Meng George Karniadakis PINN 180 759 0 13 Mar 2020