Articles

• Preface

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  245 60 Pages:i-i

• Dying ReLU and Initialization: Theory and Numerical Examples

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

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  85509 4066 Pages:1671-1706

• Finite Neuron Method and Convergence Analysis

  Jinchao Xu

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  70404 3799 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

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  86027 4254 Pages:1746-1767

• Deep Network Approximation Characterized by Number of Neurons

  Zuowei Shen, Haizhao Yang, Shijun Zhang

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  68957 3646 Pages:1768-1811

• Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression

  Yixiang Deng, Guang Lin, Xiu Yang

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  63034 3496 Pages:1812-1837

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

  Yingzhou Li, Xiuyuan Cheng, Jianfeng Lu

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  63722 3467 Pages:1838-1885

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

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

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  67253 3664 Pages:1886-1906

• Random Batch Algorithms for Quantum Monte Carlo Simulations

  Shi Jin, Xiantao Li

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  62476 3451 Pages:1907-1936

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

  Bangde Liu, Guang Lin

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  62546 3360 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

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  73856 3682 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

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  89003 4556 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

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  63919 3589 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

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  64386 3357 Pages:2109-2138

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

  Bo Wang, Wenzhong Zhang, Wei Cai

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  64332 3316 Pages:2139-2157

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

  Yufei Wang, Ziju Shen, Zichao Long, Bin Dong

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  62489 3448 Pages:2158-2179

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

  Liang Yan, Tao Zhou

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  67252 3430 Pages:2180-2205

• Machine Learning and Computational Mathematics

  Weinan E

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  88741 4333 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

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  149394 6595 Pages:2002-2041