Search Results

• An Understanding of the Physical Solutions and the Blow-up Phenomenon for Nonlinear Noisy Leaky Integrate and Fire Neuronal Models

  María J. Cáceres, Alejandro Ramos-Lora

  2021-07-01

  48141 3150 Pages:820-850

• Machine Learning and Computational Mathematics

  Weinan E

  2020-11-18

  89035 4381 Pages:1639-1670

• AutoAMG($θ$): An Auto-Tuned AMG Method Based on Deep Learning for Strong Threshold

  Haifeng Zou, Xiaowen Xu, Chen-Song Zhang, Zeyao Mo

  2024-07-29

  24682 1885 Pages:200-220

• A Data-Driven Reconstruction for Unstructured Finite Volume Method on Multi-Dimensional Compressible Flows

  Jayeon Joo, Dongseok Kim, Hojun You, Chongam Kim

  2024-12-02

  16042 1207 Pages:1307-1338

• Data-Driven, Physics-Based Feature Extraction from Fluid Flow Fields Using Convolutional Neural Networks

  Carlos Michelen Strofer, Jin-Long Wu, Heng Xiao, Eric Paterson

  2018-11-09

  66841 6246 Pages:625-650 Open-access

• A Complete Error Analysis of PINNs for Elliptic Equations Using Projected Stochastic Gradient Descent

  Yuling Jiao, Ruoxuan Li, Defeng Sun, Peiying Wu, Jerry Zhijian Yang

  2026-04-10

  243 68 Pages:27-60

• Dying ReLU and Initialization: Theory and Numerical Examples

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

  2020-11-18

  86180 4199 Pages:1671-1706

• Ensemble Gradient for Learning Turbulence Models from Indirect Observations

  Carlos A. Michelén Ströfer, Xin-Lei Zhang, Heng Xiao

  2021-10-26

  80767 3742 Pages:1269-1289

• Numerical Solution of the Incompressible Navier-Stokes Equation by a Deep Branching Algorithm

  Jiang Yu Nguwi, Guillaume Penent, Nicolas Privault

  2023-09-04

  33606 2905 Pages:261-289

• Nonlinear Reduced DNN Models for State Estimation

  Wolfgang Dahmen, Min Wang, Zhu Wang

  2022-07-06

  42942 3772 Pages:1-40

• Deep Unfitted Nitsche Method for Elliptic Interface Problems

  Hailong Guo, Xu Yang

  2022-03-30

  52740 3338 Pages:1162-1179

• Dirichlet-Neumann Learning Algorithm for Solving Elliptic Interface Problems

  Qi Sun, Xuejun Xu, Haotian Yi

  2025-07-11

  5425 679 Pages:248-284

• Deep Learning-Based Reduced-Order Methods for Fast Transient Dynamics

  Martina Cracco, Giovanni Stabile, Andrea Lario, Armin Sheidani, Martin Larcher, Folco Casadei, Georgios Valsamos, Gianluigi Rozza

  2026-01-03

  2158 190 Pages:635-660

• Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions

  Yulei Liao, Pingbing Ming

  2021-03-24

  53501 3565 Pages:1365-1384

• Convergence Analysis for Over-Parameterized Deep Learning

  Yuling Jiao, Xiliang Lu, Peiying Wu, Jerry Zhijian Yang

  2024-07-29

  28088 2178 Pages:71-103

• Deep Network Approximation Characterized by Number of Neurons

  Zuowei Shen, Haizhao Yang, Shijun Zhang

  2020-11-18

  69204 3704 Pages:1768-1811

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

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

  2020-11-18

  67430 3706 Pages:1886-1906

• Deep Potential: A General Representation of a Many-Body Potential Energy Surface

  Jiequn Han, Linfeng Zhang, Roberto Car, E. Weinan

  2018-08-21

  95388 6694 Pages:629-639 Open-access

• A Deep Spatio-Temporal Forecasting Model for Multi-Site Weather Prediction Post-Processing

  Wenjia Kong, Haochen Li, Chen Yu, Jiangjiang Xia, Yanyan Kang, Pingwen Zhang

  2021-12-06

  53751 4722 Pages:131-153

• An Augmented Lagrangian Deep Learning Method for Variational Problems with Essential Boundary Conditions

  Jianguo Huang, Haoqin Wang, Tao Zhou

  2022-03-03

  50710 3358 Pages:966-986

• A Causality-DeepONet for Causal Responses of Linear Dynamical Systems

  Lizuo Liu, Kamaljyoti Nath, Wei Cai

  2024-06-14

  36425 1892 Pages:1194-1228

• Convergence Analysis of PINNs with Over-Parameterization

  Mo Chen, Zhao Ding, Yuling Jiao, Xiliang Lu, Peiying Wu, Jerry Zhijian Yang

  2025-04-27

  9335 581 Pages:942-974

• A Correction and Comments on “Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains CiCP, 28 (5): 1970–2001, 2020”

  Lulu Zhang, Wei Cai, Zhi-Qin John Xu

  2023-06-06

  40599 2876 Pages:1509-1513