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

  DOI:10.4208/cicp.OA-2020-0130

  64587 3389 pp. 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

  DOI:10.4208/cicp.OA-2021-0257

  307217 3645 pp. 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

  DOI:10.4208/cicp.OA-2020-0193

  89565 4614 pp. 2042-2074

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

  Massimo Frittelli, Anotida Madzvamuse, Ivonne Sgura

  2023-04-28

  DOI:10.4208/cicp.OA-2022-0204

  32790 3266 pp. 733-763 Open Access

• Learning PDEs from Data on Closed Surfaces with Sparse Optimization

  Zhengjie Sun, Leevan Ling, Ran Zhang

  2025-09-02

  DOI:10.4208/cicp.OA-2024-0112

  12022 1005 pp. 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

  DOI:10.4208/cicp.OA-2023-0327

  9043 520 pp. 1383-1416

• Weak Minimization-Sampling Network for Solving PDEs

  Zhenqian E, Weiguo Gao

  2026-01-03

  DOI:10.4208/cicp.OA-2024-0153

  1940 120 pp. 696-712

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

  Shamsulhaq Basir

  2023-06-06

  DOI:10.4208/cicp.OA-2022-0239

  41861 3031 pp. 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

  DOI:10.4208/cicp.OA-2024-0096

  17522 1208 pp. 1090-1112

• Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains

  Tao Tang, Huifang Yuan, Tao Zhou

  2020-07-31

  DOI:10.4208/cicp.2018.hh80.12

  49559 4932 pp. 1143-1168 Open Access

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

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

  2022-08-11

  DOI:10.4208/cicp.OA-2021-0256

  303899 3517 pp. 336-363

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

  Wenjun Ying, Wei-Cheng Wang

  2020-07-31

  DOI:10.4208/cicp.170313.071113s

  41163 3938 pp. 1108-1140

• 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

  DOI:10.4208/cicp.OA-2023-0063

  35606 2926 pp. 813-836

• 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

  38838 3898 pp. 942-958

• Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs

  Tao Kong, Weidong Zhao, Tao Zhou

  2020-07-30

  DOI:10.4208/cicp.240515.280815a

  39424 3389 pp. 1482-1503

• Novel Symplectic Discrete Singular Convolution Method for Hamiltonian PDEs

  Wenjun Cai, Huai Zhang, Yushun Wang

  2020-07-31

  DOI:10.4208/cicp.scpde14.32s

  40658 3362 pp. 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

  DOI:10.4208/cicp.OA-2021-0092

  46274 3540 pp. 370-397

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

  Yuezheng Gong, Yushun Wang

  2020-07-30

  DOI:10.4208/cicp.231014.110416a

  42392 3560 pp. 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

  DOI:10.4208/cicp.OA-2024-0028

  15532 986 pp. 220-249

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

  Zhen Li, Zuoqiang Shi, Jian Sun

  2019-04-04

  DOI:10.4208/cicp.OA-2018-0024

  46798 3392 pp. 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

  DOI:10.4208/cicp.OA-2017-0192

  46850 3342 pp. 623-634

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

  Jiang Yu Nguwi, Guillaume Penent, Nicolas Privault

  2023-09-04

  DOI:10.4208/cicp.OA-2022-0140

  33606 2905 pp. 261-289

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

  Buyang Li, Jilu Wang, Weiwei Sun

  2020-07-31

  DOI:10.4208/cicp.080313.051213s

  42559 4374 pp. 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

  DOI:10.4208/cicp.270913.020414a

  39710 3969 pp. 571-598

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

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

  2011-09-01

  DOI:10.4208/cicp.020809.130910a

  38507 3859 pp. 1040-1055

• Simulation of Inviscid Compressible Flows Using PDE Transform

  Langhua Hu, Siyang Yang, Guo-Wei Wei

  2014-11-08

  DOI:10.4208/cicp.031113.160514a

  43318 5659 pp. 1201-1238

• Integral Regularization PINNs for Evolution Equations

  Xiaodong Feng, Haojiong Shangguan, Tao Tang, Xiaoliang Wan

  2026-02-15

  DOI:10.4208/cicp.OA-2025-0082

  4126 195 pp. 356-386