Articles

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

  Bangde Liu, Guang Lin

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  62412 3326 Pages:1937-1969

• 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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  147761 6053 Pages:2002-2041

• Machine Learning and Computational Mathematics

  Weinan E

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  88485 4276 Pages:1639-1670

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

  Liang Yan, Tao Zhou

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  67125 3405 Pages:2180-2205

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

  Yufei Wang, Ziju Shen, Zichao Long, Bin Dong

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  62322 3419 Pages:2158-2179

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

  Bo Wang, Wenzhong Zhang, Wei Cai

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  64184 3294 Pages:2139-2157

• 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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  64226 3325 Pages:2109-2138

• 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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  63767 3554 Pages:2075-2108

• 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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  88478 4440 Pages:2042-2074

• 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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  73632 3621 Pages:1970-2001

• Preface

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  119 47 Pages:i-i

• Random Batch Algorithms for Quantum Monte Carlo Simulations

  Shi Jin, Xiantao Li

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  62319 3426 Pages:1907-1936

• 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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  67104 3635 Pages:1886-1906

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

  Yingzhou Li, Xiuyuan Cheng, Jianfeng Lu

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  63549 3432 Pages:1838-1885

• Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression

  Yixiang Deng, Guang Lin, Xiu Yang

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  62881 3466 Pages:1812-1837

• Deep Network Approximation Characterized by Number of Neurons

  Zuowei Shen, Haizhao Yang, Shijun Zhang

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  68719 3581 Pages:1768-1811

• 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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  85482 4069 Pages:1746-1767

• Finite Neuron Method and Convergence Analysis

  Jinchao Xu

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  70207 3742 Pages:1707-1745

• Dying ReLU and Initialization: Theory and Numerical Examples

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

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  84943 3844 Pages:1671-1706