Search Results

• MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs

  Lulu Zhang, Tao Luo, Yaoyu Zhang, Weinan E, Zhi-Qin John Xu, Zheng Ma

  2022-08-11

  307216 3645 Pages:299-335

• 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

  2020-11-18

  64580 3388 Pages:2109-2138

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

  Jihong Wang, Xin Wang, Jing Li, Bin Liu

  2025-05-29

  9043 520 Pages:1383-1416

• A Nonlinear Elimination Preconditioner for Fully Coupled Space-Time Solution Algorithm with Applications to High-Rayleigh Number Thermal Convective Flow Problems

  Haijian Yang, Feng-Nan Hwang

  2019-04-28

  46231 3271 Pages:749-767

• Learning PDEs from Data on Closed Surfaces with Sparse Optimization

  Zhengjie Sun, Leevan Ling, Ran Zhang

  2025-09-02

  12022 1005 Pages:289-314

• The Bulk-Surface Virtual Element Method for Reaction-Diffusion PDEs: Analysis and Applications

  Massimo Frittelli, Anotida Madzvamuse, Ivonne Sgura

  2023-04-28

  32787 3266 Pages:733-763 Open-access

• Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs

  Tao Kong, Weidong Zhao, Tao Zhou

  2020-07-30

  39423 3389 Pages:1482-1503

• Long-Time Integration of Nonlinear Wave Equations with Neural Operators

  Guanhang Lei, Zhen Lei, Lei Shi

  2026-01-18

  791 145 Pages:1137-1163

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

  Jiang Yu Nguwi, Guillaume Penent, Nicolas Privault

  2023-09-04

  33602 2905 Pages:261-289

• Parareal-Richardson Algorithm for Solving Nonlinear ODEs and PDEs

  Shulin Wu, Baochang Shi, Chengming Huang

  2009-06-01

  37509 4128 Pages:883-902

• Nonlinear Stochastic Galerkin and Collocation Methods: Application to a Ferromagnetic Cylinder Rotating at High Speed

  Eveline Rosseel, Herbert De Gersem, Stefan Vandewalle

  2010-08-01

  43311 4869 Pages:947-975 Open-access

• A Local Model Reduction Method Based on $k$-Nearest-Neighbors for Parametrized Nonlocal Problems

  Caixia Nan, Qiuqi Li, Huailing Song

  2025-01-22

  15530 986 Pages:220-249

• High Order Deep Neural Network for Solving High Frequency Partial Differential Equations

  Zhipeng Chang, Ke Li, Xiufen Zou, Xueshuang Xiang

  2022-01-27

  46271 3540 Pages:370-397

• An Energy-Preserving Wavelet Collocation Method for General Multi-Symplectic Formulations of Hamiltonian PDEs

  Yuezheng Gong, Yushun Wang

  2020-07-30

  42391 3560 Pages:1313-1339

• Novel Symplectic Discrete Singular Convolution Method for Hamiltonian PDEs

  Wenjun Cai, Huai Zhang, Yushun Wang

  2020-07-31

  40658 3359 Pages:1375-1396

• 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

  151476 6984 Pages:2002-2041

• Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations

  M. J. Baines, M. E. Hubbard, P. K. Jimack

  2011-10-01

  40073 5040 Pages:509-576 Open-access

• 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

  2152 190 Pages:635-660

• A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions

  Yaqin Zhang, Ke Li, Zhipeng Chang, Xuejiao Liu, Yunqing Huang, Xueshuang Xiang

  2025-07-11

  5373 896 Pages:181-222

• A Five-Point TENO Scheme with Adaptive Dissipation Based on a New Scale Sensor

  Haohan Huang, Tian Liang, Lin Fu

  2023-05-12

  36271 3053 Pages:1106-1131

• Nonlinear Reduced DNN Models for State Estimation

  Wolfgang Dahmen, Min Wang, Zhu Wang

  2022-07-06

  42940 3769 Pages:1-40

• A Simple GPU Implementation of Spectral-Element Methods for Solving 3D Poisson Type Equations on Rectangular Domains and Its Applications

  Xinyu Liu, Jie Shen, Xiangxiong Zhang

  2024-12-02

  17143 1405 Pages:1157-1185

• Capturing Vertical Information in Radially Symmetric Flow Using Hyperbolic Shallow Water Moment Equations

  Rik Verbiest, Julian Koellermeier

  2025-09-02

  10364 571 Pages:810-848

• High Order Fixed-Point Sweeping WENO Methods for Steady State of Hyperbolic Conservation Laws and Its Convergence Study

  Liang Wu, Yong-Tao Zhang, Shuhai Zhang, Chi-Wang Shu

  2018-04-04

  40588 3220 Pages:835-869

• On Invariant-Preserving Finite Difference Schemes for the Camassa-Holm Equation and the Two-Component Camassa-Holm System

  Hailiang Liu, Terrance Pendleton

  2018-04-04

  40724 3135 Pages:1015-1041

• Explicit Multi-Symplectic Methods for Hamiltonian Wave Equations

  Jialin Hong, Shanshan Jiang, Chun Li, Hongyu Liu

  2007-02-01

  39163 3987 Pages:662-683

• An Efficient Operator-Splitting Method for Noise Removal in Images

  D. Krishnan, P. Lin, X. -C. Tai

  2006-01-01

  39578 4071 Pages:847-858