Search Results

• 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

  64386 3357 Pages:2109-2138

• 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

  307095 3600 Pages:299-335

• On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs

  Yeonjong Shin, Jérôme Darbon, George Em Karniadakis

  2020-11-18

  89003 4556 Pages:2042-2074

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

  Massimo Frittelli, Anotida Madzvamuse, Ivonne Sgura

  2023-04-28

  32683 3189 Pages:733-763 Open-access

• Learning PDEs from Data on Closed Surfaces with Sparse Optimization

  Zhengjie Sun, Leevan Ling, Ran Zhang

  2025-09-02

  11900 956 Pages:289-314

• 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

• Loss Jump During Loss Switch in Solving PDEs with Neural Networks

  Zhiwei Wang, Lulu Zhang, Zhongwang Zhang, Zhi-Qin John Xu

  2024-10-29

  17403 1163 Pages:1090-1112

• Investigating and Mitigating Failure Modes in Physics-Informed Neural Networks (PINNs)

  Shamsulhaq Basir

  2023-06-06

  41665 2977 Pages:1240-1269

• Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains

  Tao Tang, Huifang Yuan & Tao Zhou

  2020-07-31

  49420 4850 Pages:1143-1168 Open-access

• Weak Minimization-Sampling Network for Solving PDEs

  Zhenqian E, Weiguo Gao

  2026-01-03

  1690 76 Pages:696-712

• Point Integral Method for Elliptic Equations with Variable Coefficients on Point Cloud

  Zhen Li, Zuoqiang Shi & Jian Sun

  2019-04-04

  46710 3360 Pages:506-530

• The Recursive Formulation of Particular Solutions for Some Elliptic PDEs with Polynomial Source Functions

  J. Ding, H. Y. Tian & C. S. Chen

  2009-05-01

  38748 3865 Pages:942-958

• A Rate of Convergence of Weak Adversarial Neural Networks for the Second Order Parabolic PDEs

  Yuling Jiao, Jerry Zhijian Yang, Cheng Yuan, Junyu Zhou

  2023-10-07

  35482 2884 Pages:813-836

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

  Jiang Yu Nguwi, Guillaume Penent, Nicolas Privault

  2023-09-04

  33490 2855 Pages:261-289

• A Kernel-Free Boundary Integral Method for Variable Coefficients Elliptic PDEs

  Wenjun Ying & Wei-Cheng Wang

  2020-07-31

  41066 3900 Pages:1108-1140

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

  Zhipeng Chang, Ke Li, Xiufen Zou, Xueshuang Xiang

  2022-01-27

  46148 3482 Pages:370-397

• Novel Symplectic Discrete Singular Convolution Method for Hamiltonian PDEs

  Wenjun Cai, Huai Zhang & Yushun Wang

  2020-07-31

  40570 3323 Pages:1375-1396

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

  Yuezheng Gong & Yushun Wang

  2020-07-30

  42297 3523 Pages:1313-1339

• Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs

  Tao Kong, Weidong Zhao & Tao Zhou

  2020-07-30

  39341 3361 Pages:1482-1503

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

  Caixia Nan, Qiuqi Li, Huailing Song

  2025-01-22

  15404 898 Pages:220-249

• Nonstandard Fourier Pseudospectral Time Domain (PSTD) Schemes for Partial Differential Equations

  Bradley E. Treeby, Elliott S. Wise & B. T. Cox

  2018-09-17

  46725 3302 Pages:623-634

• Frame Invariance and Scalability of Neural Operators for Partial Differential Equations

  Muhammad I. Zafar, Jiequn Han, Xu-Hui Zhou, Heng Xiao

  2022-08-11

  303796 3475 Pages:336-363

• The Stability and Convergence of Fully Discrete Galerkin-Galerkin FEMs for Porous Medium Flows

  Buyang Li, Jilu Wang & Weiwei Sun

  2020-07-31

  42467 4331 Pages:1141-1158

• An Adaptive ANOVA-Based Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficient

  Zhiwen Zhang, Xin Hu, Thomas Y. Hou, Guang Lin & Mike Yan

  2014-12-08

  39606 3927 Pages:571-598

• Simulation of Inviscid Compressible Flows Using PDE Transform

  Langhua Hu, Siyang Yang & Guo-Wei Wei

  2014-11-08

  43233 5627 Pages:1201-1238

• Modified Baer-Nunziato Model for the Simulation of Interfaces Between Compressible Fluids

  Qiang Wu, Xian-Guo Lu & De-Kang Mao

  2011-09-01

  38427 3823 Pages:1040-1055

• Integral Regularization PINNs for Evolution Equations

  Xiaodong Feng, Haojiong Shangguan, Tao Tang, Xiaoliang Wan

  2026-02-15

  3808 139 Pages:356-386