Machine Learning and Computational Mathematics
Weinan E

Dying ReLU and Initialization: Theory and Numerical Examples
Lu Lu, Yeonjong Shin, Yanhui Su & George Em Karniadakis

Finite Neuron Method and Convergence Analysis
Jinchao Xu

Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks
Zhi-Qin John Xu, Yaoyu Zhang, Tao Luo, Yanyang Xiao & Zheng Ma

Deep Network Approximation Characterized by Number of Neurons
Zuowei Shen, Haizhao Yang & Shijun Zhang

Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression
Yixiang Deng, Guang Lin & Xiu Yang

Butterfly-Net: Optimal Function Representation Based on Convolutional Neural Networks
Yingzhou Li, Xiuyuan Cheng & Jianfeng Lu

A Multi-Scale DNN Algorithm for Nonlinear Elliptic Equations with Multiple Scales
Xi-An Li, Zhi-Qin John Xu & Lei Zhang

Random Batch Algorithms for Quantum Monte Carlo Simulations
Shi Jin & Xiantao Li

High-Dimensional Nonlinear Multi-Fidelity Model with Gradient-Free Active Subspace Method
Bangde Liu & Guang Lin

Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains
Ziqi Liu, Wei Cai & Zhi-Qin John Xu

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

On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
Yeonjong Shin, Jérôme Darbon & George Em Karniadakis

Convolution Neural Network Shock Detector for Numerical Solution of Conservation Laws
Zheng Sun, Shuyi Wang, Lo-Bin Chang, Yulong Xing & Dongbin Xiu

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

Multi-Scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains
Bo Wang, Wenzhong Zhang & Wei Cai

Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learning
Yufei Wang, Ziju Shen, Zichao Long & Bin Dong

An Adaptive Surrogate Modeling Based on Deep Neural Networks for Large-Scale Bayesian Inverse Problems
Liang Yan & Tao Zhou