Deep Neural Network Modeling of Unknown Partial Differential Equations
in Nodal Space

Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space

7 June 2021

Papers citing "Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space"

15 / 15 papers shown

Title
Data-driven learning of non-autonomous systems Tong Qin Zhen Chen J. Jakeman D. Xiu 37 19 0 02 Jun 2020
Learning reduced systems via deep neural networks with memory Xiaohang Fu L. Chang D. Xiu 36 32 0 20 Mar 2020
Data-Driven Deep Learning of Partial Differential Equations in Modal Space Kailiang Wu D. Xiu 106 152 0 15 Oct 2019
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators Lu Lu Pengzhan Jin George Karniadakis 222 2,119 0 08 Oct 2019
NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data Yifan Sun Linan Zhang Hayden Schaeffer AI4TS 52 91 0 08 Aug 2019
Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data Kailiang Wu Tong Qin D. Xiu 43 31 0 24 May 2019
PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network Zichao Long Yiping Lu Bin Dong AI4CE 65 552 0 30 Nov 2018
Data Driven Governing Equations Approximation Using Deep Neural Networks Tong Qin Kailiang Wu D. Xiu PINN 62 273 0 13 Nov 2018
Numerical Aspects for Approximating Governing Equations Using Data Kailiang Wu D. Xiu 42 68 0 24 Sep 2018
Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations M. Raissi PINN AI4CE 112 754 0 20 Jan 2018
Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems M. Raissi P. Perdikaris George Karniadakis PINN 141 266 0 04 Jan 2018
Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations M. Raissi P. Perdikaris George Karniadakis PINN AI4CE 78 613 0 28 Nov 2017
Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations M. Raissi P. Perdikaris George Karniadakis PINN AI4CE 75 924 0 28 Nov 2017
PDE-Net: Learning PDEs from Data Zichao Long Yiping Lu Xianzhong Ma Bin Dong DiffM AI4CE 38 755 0 26 Oct 2017
Deep Residual Learning for Image Recognition Kaiming He Xinming Zhang Shaoqing Ren Jian Sun MedIm 2.2K 193,814 0 10 Dec 2015