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Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations

Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations

Chuqi Chen
Yahong Yang
Yang Xiang
Wenrui Hao
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Papers citing "Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations"

15 / 15 papers shown
Title
Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss
Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss
Yahong Yang
Juncai He
AI4CE
183
7
0
31 Jan 2024
Homotopy Relaxation Training Algorithms for Infinite-Width Two-Layer ReLU Neural Networks
Homotopy Relaxation Training Algorithms for Infinite-Width Two-Layer ReLU Neural Networks
Yahong Yang
Qipin Chen
Wenrui Hao
49
4
0
26 Sep 2023
Nearly Optimal VC-Dimension and Pseudo-Dimension Bounds for Deep Neural Network Derivatives
Nearly Optimal VC-Dimension and Pseudo-Dimension Bounds for Deep Neural Network Derivatives
Yahong Yang
Haizhao Yang
Yang Xiang
60
20
0
15 May 2023
DOSnet as a Non-Black-Box PDE Solver: When Deep Learning Meets Operator Splitting
DOSnet as a Non-Black-Box PDE Solver: When Deep Learning Meets Operator Splitting
Yuan Lan
Zerui Li
Jie Sun
Yang Xiang
44
11
0
11 Dec 2022
Transformer Meets Boundary Value Inverse Problems
Transformer Meets Boundary Value Inverse Problems
Ruchi Guo
Shuhao Cao
Long Chen
MedIm
65
22
0
29 Sep 2022
CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method
CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method
P. Chiu
Jian Cheng Wong
C. Ooi
M. Dao
Yew-Soon Ong
PINN
50
214
0
29 Oct 2021
Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs
Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs
Tim De Ryck
Siddhartha Mishra
PINN
67
101
0
28 Jun 2021
Choose a Transformer: Fourier or Galerkin
Choose a Transformer: Fourier or Galerkin
Shuhao Cao
69
245
0
31 May 2021
Finite Volume Neural Network: Modeling Subsurface Contaminant Transport
Finite Volume Neural Network: Modeling Subsurface Contaminant Transport
T. Praditia
Matthias Karlbauer
S. Otte
S. Oladyshkin
Martin Volker Butz
Wolfgang Nowak
AI4CE
47
18
0
13 Apr 2021
Teaching the Incompressible Navier-Stokes Equations to Fast Neural Surrogate Models in 3D
Teaching the Incompressible Navier-Stokes Equations to Fast Neural Surrogate Models in 3D
Nils Wandel
Michael Weinmann
Reinhard Klein
AI4CE
64
51
0
22 Dec 2020
Deep Network Approximation for Smooth Functions
Deep Network Approximation for Smooth Functions
Jianfeng Lu
Zuowei Shen
Haizhao Yang
Shijun Zhang
105
247
0
09 Jan 2020
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems
E. Weinan
Ting Yu
119
1,387
0
30 Sep 2017
An overview of gradient descent optimization algorithms
An overview of gradient descent optimization algorithms
Sebastian Ruder
ODL
204
6,188
0
15 Sep 2016
Automatic differentiation in machine learning: a survey
Automatic differentiation in machine learning: a survey
A. G. Baydin
Barak A. Pearlmutter
Alexey Radul
J. Siskind
PINN
AI4CE
ODL
160
2,803
0
20 Feb 2015
Adam: A Method for Stochastic Optimization
Adam: A Method for Stochastic Optimization
Diederik P. Kingma
Jimmy Ba
ODL
1.8K
150,115
0
22 Dec 2014

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