Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using
Physics-Informed Neural Networks

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Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

3 May 2019

George Karniadakis

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Papers citing "Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks"

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Title
Physics Informed Deep Kernel Learning Ziyi Wang Wei W. Xing Robert M. Kirby Shandian Zhe PINN 53 10 0 08 Jun 2020
RoeNets: Predicting Discontinuity of Hyperbolic Systems from Continuous Data S. Xiong Xingzhe He Yunjin Tong Runze Liu Bo Zhu AI4CE 16 4 0 07 Jun 2020
Deep learning of free boundary and Stefan problems Sizhuang He P. Perdikaris 135 85 0 04 Jun 2020
Neural Network Solutions to Differential Equations in Non-Convex Domains: Solving the Electric Field in the Slit-Well Microfluidic Device M. Magill Andrew M. Nagel H. D. de Haan 29 7 0 25 Apr 2020
Structure-preserving neural networks Quercus Hernandez Alberto Badías D. González Francisco Chinesta Elías Cueto PINN 129 71 0 09 Apr 2020
On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs Yeonjong Shin Jérome Darbon George Karniadakis PINN 73 79 0 03 Apr 2020
Mean-Field and Kinetic Descriptions of Neural Differential Equations Michael Herty T. Trimborn G. Visconti 118 6 0 07 Jan 2020
PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs Xuhui Meng Zhen Li Dongkun Zhang George Karniadakis PINN AI4CE 90 456 0 23 Sep 2019
Learning the Tangent Space of Dynamical Instabilities from Data Antoine Blanchard T. Sapsis 134 8 0 24 Jul 2019
DeepXDE: A deep learning library for solving differential equations Lu Lu Xuhui Meng Zhiping Mao George Karniadakis PINN AI4CE 101 1,554 0 10 Jul 2019