Articles

• Preface

  • Preview
  • Requires Subscription or Fee Full PDF

  382 105 Pages:i-i

• Dying ReLU and Initialization: Theory and Numerical Examples

  Lu Lu, Yeonjong Shin, Yanhui Su, George Em Karniadakis

  • Preview
  • Requires Subscription or Fee Full PDF

  86180 4199 Pages:1671-1706

• Finite Neuron Method and Convergence Analysis

  Jinchao Xu

  • Preview
  • Requires Subscription or Fee Full PDF

  70604 3843 Pages:1707-1745

• Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks

  Zhi-Qin John Xu, Yaoyu Zhang, Tao Luo, Yanyang Xiao, Zheng Ma

  • Preview
  • Requires Subscription or Fee Full PDF

  86804 4378 Pages:1746-1767

• Deep Network Approximation Characterized by Number of Neurons

  Zuowei Shen, Haizhao Yang, Shijun Zhang

  • Preview
  • Requires Subscription or Fee Full PDF

  69204 3704 Pages:1768-1811

• Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression

  Yixiang Deng, Guang Lin, Xiu Yang

  • Preview
  • Requires Subscription or Fee Full PDF

  63219 3530 Pages:1812-1837

• Butterfly-Net: Optimal Function Representation Based on Convolutional Neural Networks

  Yingzhou Li, Xiuyuan Cheng, Jianfeng Lu

  • Preview
  • Requires Subscription or Fee Full PDF

  63895 3512 Pages:1838-1885

• A Multi-Scale DNN Algorithm for Nonlinear Elliptic Equations with Multiple Scales

  Xi-An Li, Zhi-Qin John Xu, Lei Zhang

  • Preview
  • Requires Subscription or Fee Full PDF

  67430 3706 Pages:1886-1906

• Random Batch Algorithms for Quantum Monte Carlo Simulations

  Shi Jin, Xiantao Li

  • Preview
  • Requires Subscription or Fee Full PDF

  62637 3510 Pages:1907-1936

• High-Dimensional Nonlinear Multi-Fidelity Model with Gradient-Free Active Subspace Method

  Bangde Liu, Guang Lin

  • Preview
  • Requires Subscription or Fee Full PDF

  62704 3396 Pages:1937-1969

• Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains

  Ziqi Liu, Wei Cai, Zhi-Qin John Xu

  • Preview
  • Requires Subscription or Fee Full PDF

  74201 3754 Pages:1970-2001

• On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs

  Yeonjong Shin, Jérôme Darbon, George Em Karniadakis

  • Preview
  • Requires Subscription or Fee Full PDF

  89565 4614 Pages:2042-2074

• Convolution Neural Network Shock Detector for Numerical Solution of Conservation Laws

  Zheng Sun, Shuyi Wang, Lo-Bin Chang, Yulong Xing, Dongbin Xiu

  • Preview
  • Requires Subscription or Fee Full PDF

  64108 3617 Pages:2075-2108

• Numerical Simulations for Full History Recursive Multilevel Picard Approximations for Systems of High-Dimensional Partial Differential Equations

  Sebastian Becker, Ramon Braunwarth, Martin Hutzenthaler, Arnulf Jentzen, Philippe von Wurstemberger

  • Preview
  • Requires Subscription or Fee Full PDF

  64587 3389 Pages:2109-2138

• Multi-Scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains

  Bo Wang, Wenzhong Zhang, Wei Cai

  • Preview
  • Requires Subscription or Fee Full PDF

  64576 3363 Pages:2139-2157

• Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learning

  Yufei Wang, Ziju Shen, Zichao Long, Bin Dong

  • Preview
  • Requires Subscription or Fee Full PDF

  62676 3497 Pages:2158-2179

• An Adaptive Surrogate Modeling Based on Deep Neural Networks for Large-Scale Bayesian Inverse Problems

  Liang Yan, Tao Zhou

  • Preview
  • Requires Subscription or Fee Full PDF

  67487 3473 Pages:2180-2205

• Machine Learning and Computational Mathematics

  Weinan E

  • Preview
  • Requires Subscription or Fee Full PDF

  89035 4381 Pages:1639-1670

• Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

  Ameya D. Jagtap, George Em Karniadakis

  • Preview
  • Requires Subscription or Fee Full PDF

  151550 6990 Pages:2002-2041