TSONN: Time-stepping-oriented neural network for solving partial differential equations

25 October 2023

Papers citing "TSONN: Time-stepping-oriented neural network for solving partial differential equations"

18 / 18 papers shown

Title
Can Physics-Informed Neural Networks beat the Finite Element Method? T. G. Grossmann Urszula Julia Komorowska J. Latz Carola-Bibiane Schönlieb PINN AI4CE 103 92 0 08 Feb 2023
A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks Chen-Chun Wu Min Zhu Qinyan Tan Yadhu Kartha Lu Lu 99 383 0 21 Jul 2022
Learning to correct spectral methods for simulating turbulent flows Gideon Dresdner Dmitrii Kochkov Peter C. Norgaard Leonardo Zepeda-Núñez Jamie A. Smith M. Brenner Stephan Hoyer AI4CE 71 62 0 01 Jul 2022
Respecting causality is all you need for training physics-informed neural networks Sizhuang He Shyam Sankaran P. Perdikaris PINN CML AI4CE 150 203 0 14 Mar 2022
Physics-informed neural networks (PINNs) for fluid mechanics: A review Shengze Cai Zhiping Mao Zhicheng Wang Minglang Yin George Karniadakis PINN AI4CE 88 1,209 0 20 May 2021
Efficient training of physics-informed neural networks via importance sampling M. A. Nabian R. J. Gladstone Hadi Meidani DiffM PINN 130 237 0 26 Apr 2021
Parallel Physics-Informed Neural Networks via Domain Decomposition K. Shukla Ameya Dilip Jagtap George Karniadakis PINN 173 286 0 20 Apr 2021
Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism L. McClenny U. Braga-Neto PINN 92 461 0 07 Sep 2020
When and why PINNs fail to train: A neural tangent kernel perspective Sizhuang He Xinling Yu P. Perdikaris 141 924 0 28 Jul 2020
Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks Colby Wight Jia Zhao 80 225 0 09 Jul 2020
PFNN: A Penalty-Free Neural Network Method for Solving a Class of Second-Order Boundary-Value Problems on Complex Geometries H. Sheng Chao Yang 61 118 0 14 Apr 2020
D3M: A deep domain decomposition method for partial differential equations Ke Li Keju Tang Tianfan Wu Qifeng Liao AI4CE 84 117 0 24 Sep 2019
PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs Xuhui Meng Zhen Li Dongkun Zhang George Karniadakis PINN AI4CE 84 456 0 23 Sep 2019
An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications E. Samaniego C. Anitescu S. Goswami Vien Minh Nguyen-Thanh Hongwei Guo Khader M. Hamdia Timon Rabczuk X. Zhuang PINN AI4CE 234 1,389 0 27 Aug 2019
Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks Zhi-Qin John Xu Yaoyu Zhang Yaoyu Zhang Yan Xiao Zheng Ma 133 520 0 19 Jan 2019
Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data M. Raissi A. Yazdani George Karniadakis AI4CE PINN 96 161 0 13 Aug 2018
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 130 1,393 0 30 Sep 2017
Automatic differentiation in machine learning: a survey A. G. Baydin Barak A. Pearlmutter Alexey Radul J. Siskind PINN AI4CE ODL 181 2,824 0 20 Feb 2015