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

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

23 May 2024

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 Yahong Yang Juncai He AI4CE 128 7 0 31 Jan 2024
Homotopy Relaxation Training Algorithms for Infinite-Width Two-Layer ReLU Neural Networks Yahong Yang Qipin Chen Wenrui Hao 34 4 0 26 Sep 2023
Nearly Optimal VC-Dimension and Pseudo-Dimension Bounds for Deep Neural Network Derivatives Yahong Yang Haizhao Yang Yang Xiang 56 20 0 15 May 2023
DOSnet as a Non-Black-Box PDE Solver: When Deep Learning Meets Operator Splitting Yuan Lan Zerui Li Jie Sun Yang Xiang 41 11 0 11 Dec 2022
Transformer Meets Boundary Value Inverse Problems Ruchi Guo Shuhao Cao Long Chen MedIm 56 21 0 29 Sep 2022
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 46 210 0 29 Oct 2021
Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs Tim De Ryck Siddhartha Mishra PINN 55 100 0 28 Jun 2021
Choose a Transformer: Fourier or Galerkin Shuhao Cao 58 237 0 31 May 2021
Finite Volume Neural Network: Modeling Subsurface Contaminant Transport T. Praditia Matthias Karlbauer S. Otte S. Oladyshkin Martin Volker Butz Wolfgang Nowak AI4CE 34 18 0 13 Apr 2021
Teaching the Incompressible Navier-Stokes Equations to Fast Neural Surrogate Models in 3D Nils Wandel Michael Weinmann Reinhard Klein AI4CE 56 50 0 22 Dec 2020
Deep Network Approximation for Smooth Functions Jianfeng Lu Zuowei Shen Haizhao Yang Shijun Zhang 87 247 0 09 Jan 2020
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 97 1,373 0 30 Sep 2017
An overview of gradient descent optimization algorithms Sebastian Ruder ODL 177 6,170 0 15 Sep 2016
Automatic differentiation in machine learning: a survey A. G. Baydin Barak A. Pearlmutter Alexey Radul J. Siskind PINN AI4CE ODL 129 2,775 0 20 Feb 2015
Adam: A Method for Stochastic Optimization Diederik P. Kingma Jimmy Ba ODL 806 149,474 0 22 Dec 2014