Articles

• Preface

  i-i

  • Preview
  • Requires Subscription Full PDF

  119 47

• Dying ReLU and Initialization: Theory and Numerical Examples

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

  1671-1706

  https://doi.org/10.4208/cicp.OA-2020-0165

  • Preview
  • Requires Subscription Full PDF

  84934 3842

• Finite Neuron Method and Convergence Analysis

  Jinchao Xu

  1707-1745

  https://doi.org/10.4208/cicp.OA-2020-0191

  • Preview
  • Requires Subscription Full PDF

  70207 3742

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

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

  1746-1767

  https://doi.org/10.4208/cicp.OA-2020-0085

  • Preview
  • Requires Subscription Full PDF

  85473 4069

• Deep Network Approximation Characterized by Number of Neurons

  Zuowei Shen, Haizhao Yang, Shijun Zhang

  1768-1811

  https://doi.org/10.4208/cicp.OA-2020-0149

  • Preview
  • Requires Subscription Full PDF

  68719 3581

• Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression

  Yixiang Deng, Guang Lin, Xiu Yang

  1812-1837

  https://doi.org/10.4208/cicp.OA-2020-0151

  • Preview
  • Requires Subscription Full PDF

  62880 3465

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

  Yingzhou Li, Xiuyuan Cheng, Jianfeng Lu

  1838-1885

  https://doi.org/10.4208/cicp.OA-2020-0214

  • Preview
  • Requires Subscription Full PDF

  63546 3431

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

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

  1886-1906

  https://doi.org/10.4208/cicp.OA-2020-0187

  • Preview
  • Requires Subscription Full PDF

  67098 3635

• Random Batch Algorithms for Quantum Monte Carlo Simulations

  Shi Jin, Xiantao Li

  1907-1936

  https://doi.org/10.4208/cicp.OA-2020-0168

  • Preview
  • Requires Subscription Full PDF

  62318 3426

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

  Bangde Liu, Guang Lin

  1937-1969

  https://doi.org/10.4208/cicp.OA-2020-0195

  • Preview
  • Requires Subscription Full PDF

  62412 3326

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

  Ziqi Liu, Wei Cai, Zhi-Qin John Xu

  1970-2001

  https://doi.org/10.4208/cicp.OA-2020-0179

  • Preview
  • Requires Subscription Full PDF

  73630 3620

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

  Yeonjong Shin, Jérôme Darbon, George Em Karniadakis

  2042-2074

  https://doi.org/10.4208/cicp.OA-2020-0193

  • Preview
  • Requires Subscription Full PDF

  88470 4439

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

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

  2075-2108

  https://doi.org/10.4208/cicp.OA-2020-0199

  • Preview
  • Requires Subscription Full PDF

  63767 3554

• 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

  2109-2138

  https://doi.org/10.4208/cicp.OA-2020-0130

  • Preview
  • Requires Subscription Full PDF

  64222 3324

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

  Bo Wang, Wenzhong Zhang, Wei Cai

  2139-2157

  https://doi.org/10.4208/cicp.OA-2020-0192

  • Preview
  • Requires Subscription Full PDF

  64184 3294

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

  Yufei Wang, Ziju Shen, Zichao Long, Bin Dong

  2158-2179

  https://doi.org/10.4208/cicp.OA-2020-0194

  • Preview
  • Requires Subscription Full PDF

  62322 3417

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

  Liang Yan, Tao Zhou

  2180-2205

  https://doi.org/10.4208/cicp.OA-2020-0186

  • Preview
  • Requires Subscription Full PDF

  67122 3404

• Machine Learning and Computational Mathematics

  Weinan E

  1639-1670

  https://doi.org/10.4208/cicp.OA-2020-0185

  • Preview
  • Requires Subscription Full PDF

  88485 4274

• 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

  2002-2041

  https://doi.org/10.4208/cicp.OA-2020-0164

  • Preview
  • Requires Subscription Full PDF

  147729 6046