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

  64226 3325 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

  306975 3553 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

  88478 4440 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

  32547 3098 Pages:733-763 Open-access

• Learning PDEs from Data on Closed Surfaces with Sparse Optimization

  Zhengjie Sun, Leevan Ling, Ran Zhang

  2025-09-02

  182 58 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

  194 50 Pages:1383-1416

• Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains

  Tao Tang, Huifang Yuan & Tao Zhou

  2020-07-31

  49313 4810 Pages:1143-1168 Open-access

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

  Shamsulhaq Basir

  2023-06-06

  41484 2933 Pages:1240-1269

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

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

  2024-10-29

  146 60 Pages:1090-1112

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

  Wenjun Ying & Wei-Cheng Wang

  2020-07-31

  40996 3866 Pages:1108-1140

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

  Jiang Yu Nguwi, Guillaume Penent, Nicolas Privault

  2023-09-04

  33381 2823 Pages:261-289

• 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

  35332 2836 Pages:813-836

• Novel Symplectic Discrete Singular Convolution Method for Hamiltonian PDEs

  Wenjun Cai, Huai Zhang & Yushun Wang

  2020-07-31

  40513 3304 Pages:1375-1396

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

  Zhipeng Chang, Ke Li, Xiufen Zou, Xueshuang Xiang

  2022-01-27

  46031 3436 Pages:370-397

• 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

  38665 3831 Pages:942-958

• Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs

  Tao Kong, Weidong Zhao & Tao Zhou

  2020-07-30

  39282 3341 Pages:1482-1503

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

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

  2022-08-11

  303702 3397 Pages:336-363

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

  Zhen Li, Zuoqiang Shi & Jian Sun

  2019-04-04

  46615 3334 Pages:506-530

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

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

  2018-09-17

  46602 3271 Pages:623-634

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

  Yuezheng Gong & Yushun Wang

  2020-07-30

  42209 3501 Pages:1313-1339

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

  Caixia Nan, Qiuqi Li, Huailing Song

  2025-01-22

  188 120 Pages:220-249

• Simulation of Inviscid Compressible Flows Using PDE Transform

  Langhua Hu, Siyang Yang & Guo-Wei Wei

  2014-11-08

  43159 5609 Pages:1201-1238

• 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

  39540 3893 Pages:571-598

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

  Buyang Li, Jilu Wang & Weiwei Sun

  2020-07-31

  42403 4297 Pages:1141-1158

• On the Gauss Runge-Kutta and Method of Lines Transpose for Initial-Boundary Value Parabolic PDEs

  Bo Zhang, Dangxing Chen & Jingfang Huang

  2020-07-31

  42641 3230 Pages:1221-1240

• Asymptotic Results of Schwarz Waveform Relaxation Algorithm for Time Fractional Cable Equations

  Shu-Lin Wu & Chengming Huang

  2018-10-11

  44325 3412 Pages:390-415

• Two-Scale Neural Networks for Partial Differential Equations with Small Parameters

  Qiao Zhuang, Chris Ziyi Yao, Zhongqiang Zhang, George Em Karniadakis

  2025-08-23

  6003 511 Pages:603-629