Search Results

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

  Yufei Wang, Ziju Shen, Zichao Long, Bin Dong

  2020-11-18

  62489 3448 Pages:2158-2179

• Accurate Adaptive Deep Learning Method for Solving Elliptic Problems

  Jinyong Ying, Yaqi Xie, Jiao Li, Hongqiao Wang

  2025-09-02

  10230 558 Pages:849-876

• Deep Learning-Based Computational Method for Soft Matter Dynamics: Deep Onsager-Machlup Method

  Zhihao Li, Boyi Zou, Haiqin Wang, Jian Su, Dong Wang, Xinpeng Xu

  2025-09-02

  11749 752 Pages:353-382

• DL-PDE: Deep-Learning Based Data-Driven Discovery of Partial Differential Equations from Discrete and Noisy Data

  Hao Xu, Haibin Chang, Dongxiao Zhang

  2021-01-13

  55176 3525 Pages:698-728

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

  Jianguo Huang, Haoqin Wang, Tao Zhou

  2022-03-03

  50575 3314 Pages:966-986

• 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

  1892 137 Pages:635-660

• Convergence Analysis for Over-Parameterized Deep Learning

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

  2024-07-29

  27948 2069 Pages:71-103

• Generalization Error in the Deep Ritz Method with Smooth Activation Functions

  Janne Siipola

  2024-04-10

  24248 2315 Pages:761-815 Open-access

• Convergence Rate Analysis for Deep Ritz Method

  Chenguang Duan, Yuling Jiao, Yanming Lai, Dingwei Li, Xiliang Lu, Jerry Zhijian Yang

  2022-03-30

  58970 3389 Pages:1020-1048

• Physics-Driven Learning of the Steady Navier-Stokes Equations Using Deep Convolutional Neural Networks

  Hao Ma, Yuxuan Zhang, Nils Thuerey, Xiangyu Hu, Oskar J. Haidn

  2022-09-29

  42769 3348 Pages:715-736

• Newton’s Method and Its Hybrid with Machine Learning for Navier-Stokes Darcy Models Discretized by Mixed Element Methods

  Jianguo Huang, Hui Peng, Haohao Wu

  2025-01-22

  15867 892 Pages:30-60

• Data Generation-Based Operator Learning for Solving Partial Differential Equations on Unbounded Domains

  Jihong Wang, Xin Wang, Jing Li, Bin Liu

  2025-05-29

  8885 481 Pages:1383-1416

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

  Yulei Liao, Pingbing Ming

  2021-03-24

  53300 3485 Pages:1365-1384

• A Deep Learning Modeling Framework to Capture Mixing Patterns in Reactive-Transport Systems

  N. V. Jagtap, M. K. Mudunuru, K. B. Nakshatrala

  2021-12-06

  49367 4042 Pages:188-223

• Ensemble Gradient for Learning Turbulence Models from Indirect Observations

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

  2021-10-26

  80671 3711 Pages:1269-1289

• Deep Unfitted Nitsche Method for Elliptic Interface Problems

  Hailong Guo, Xu Yang

  2022-03-30

  52625 3284 Pages:1162-1179

• 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

  2020-11-18

  149394 6595 Pages:2002-2041

• Dirichlet-Neumann Learning Algorithm for Solving Elliptic Interface Problems

  Qi Sun, Xuejun Xu, Haotian Yi

  2025-07-11

  5279 579 Pages:248-284

• Local Discontinuous Galerkin Method for Nonlinear BSPDEs of Neumann Boundary Conditions with Deep Backward Dynamic Programming Time-Marching

  Yixiang Dai, Yunzhang Li, Jing Zhang

  2026-01-18

  237 46 Pages:1299-1331

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

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

  2020-11-18

  86027 4254 Pages:1746-1767

• Learning Specialized Activation Functions for Physics-Informed Neural Networks

  Honghui Wang, Lu Lu, Shiji Song, Gao Huang

  2023-11-08

  34553 2896 Pages:869-906

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

  Yingzhou Li, Xiuyuan Cheng, Jianfeng Lu

  2020-11-18

  63722 3467 Pages:1838-1885

• 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

  24538 1767 Pages:200-220

• Continuous-Variable Deep Quantum Neural Networks for Flexible Learning of Structured Classical Information

  Jasvith Raj Basani, Aranya Bhattacherjee

  2021-08-10

  46210 2995 Pages:1216-1231

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

  Ziqi Liu, Wei Cai, Zhi-Qin John Xu

  2020-11-18

  73856 3682 Pages:1970-2001

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

  Bo Wang, Wenzhong Zhang, Wei Cai

  2020-11-18

  64332 3316 Pages:2139-2157

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

  Jiequn Han, Linfeng Zhang, Roberto Car & Weinan E

  2018-08-21

  94955 6552 Pages:629-639 Open-access