Search Results

• A Complete Error Analysis of PINNs for Elliptic Equations Using Projected Stochastic Gradient Descent

  Yuling Jiao, Ruoxuan Li, Defeng Sun, Peiying Wu, Jerry Zhijian Yang

  2026-04-10

  DOI:10.4208/cicp.OA-2025-0102

  243 68 pp. 27-60

• A Neural Particle Method with Interface Tracking and Adaptive Particle Refinement for Free Surface Flows

  Pei-Hsin Pai, Heng-Chuan Kan, Hock-Kiet Wong, Yih-Chin Tai

  2024-10-29

  DOI:10.4208/cicp.OA-2023-0235

  17866 1218 pp. 1021-1052

• Neural Networks with Local Converging Inputs (NNLCI) for Solving Conservation Laws, Part I: 1D Problems

  Haoxiang Huang, Vigor Yang, Yingjie Liu

  2023-09-04

  DOI:10.4208/cicp.OA-2022-0285

  35668 2891 pp. 290-317

• Benchmark Computation of Morphological Complexity in the Functionalized Cahn-Hilliard Gradient Flow

  Andrew Christlieb, Keith Promislow, Zengqiang Tan, Sulin Wang, Brian Wetton, Steven M. Wise

  2025-04-27

  DOI:10.4208/cicp.OA-2023-0190

  9418 836 pp. 877-920 Open Access

• Opinion Dynamics of Sznajd Model on Small-World Network

  L. Guo, X. Cai

  2009-06-01

  39863 4178 pp. 586-594

• 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

  DOI:10.4208/cicp.OA-2023-0294

  11909 813 pp. 353-382

• Hamiltonian Reduction Using a Convolutional Auto-Encoder Coupled to a Hamiltonian Neural Network

  Raphaël Côte, Emmanuel Franck, Laurent Navoret, Guillaume Steimer, Vincent Vigon

  2025-09-02

  DOI:10.4208/cicp.OA-2023-0300

  11896 916 pp. 315-352

• Computationally Efficient Fluid-Particle Dynamics Simulations of Arterial Systems

  Tejas S. Umbarkar, Clement Kleinstreuer

  2020-07-30

  DOI:10.4208/cicp.160114.120914a

  40648 3035 pp. 401-423

• 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

  DOI:10.4208/cicp.OA-2020-0142

  55435 3561 pp. 698-728

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

  Yulei Liao, Pingbing Ming

  2021-03-24

  DOI:10.4208/cicp.OA-2020-0219

  53501 3565 pp. 1365-1384

• Dirichlet-Neumann Learning Algorithm for Solving Elliptic Interface Problems

  Qi Sun, Xuejun Xu, Haotian Yi

  2025-07-11

  DOI:10.4208/cicp.OA-2024-0046

  5425 679 pp. 248-284

• Convergence Analysis of PINNs with Over-Parameterization

  Mo Chen, Zhao Ding, Yuling Jiao, Xiliang Lu, Peiying Wu, Jerry Zhijian Yang

  2025-04-27

  DOI:10.4208/cicp.OA-2023-0101

  9335 581 pp. 942-974

• Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability

  Zhen Gao, Qi Liu, Jan S. Hesthaven, Bao-Shan Wang, Wai Sun Don, Xiao Wen

  2021-04-30

  DOI:10.4208/cicp.OA-2020-0064

  50093 4593 pp. 97-123

• A Data-Driven Scale-Invariant Weighted Compact Nonlinear Scheme for Hyperbolic Conservation Laws

  Zixuan Zhang, Yidao Dong, Yuanyang Zou, Hao Zhang, Xiaogang Deng

  2024-05-06

  DOI:10.4208/cicp.OA-2023-0162

  28544 2086 pp. 1120-1154

• 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

• A Conservative and Positivity-Preserving Method for Solving Anisotropic Diffusion Equations with Deep Learning

  Hui Xie, Li Liu, Chuanlei Zhai, Xuejun Xu, Heng Yong

  2024-03-13

  DOI:10.4208/cicp.OA-2023-0180

  26439 2329 pp. 467-497

• Deep Unfitted Nitsche Method for Elliptic Interface Problems

  Hailong Guo, Xu Yang

  2022-03-30

  DOI:10.4208/cicp.OA-2021-0201

  52740 3338 pp. 1162-1179

• Bi-Orthogonal fPINN: A Physics-Informed Neural Network Method for Solving Time-Dependent Stochastic Fractional PDEs

  Lei Ma, Rongxin Li, Fanhai Zeng, Ling Guo, George Em Karniadakis

  2023-11-08

  DOI:10.4208/cicp.OA-2023-0075

  32040 2870 pp. 1133-1176

• 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

• Effects of Complex System Topology on the Bak-Sneppen Evolution Model

  L. Guo, X. Cai

  2010-07-01

  DOI:10.4208/cicp.2009.09.075

  39617 4146 pp. 534-543

• An Efficient Neural-Network and Finite-Difference Hybrid Method for Elliptic Interface Problems with Applications

  Wei-Fan Hu, Te-Sheng Lin, Yu-Hau Tseng, Ming-Chih Lai

  2023-05-12

  DOI:10.4208/cicp.OA-2022-0284

  36494 2927 pp. 1090-1105

• 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

  DOI:10.4208/cicp.OA-2024-0095

  5374 896 pp. 181-222

• 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

• Numerical Calculation of Equivalent Permeability Tensor for Fractured Vuggy Porous Media Based on Homogenization Theory

  Zhaoqin Huang, Jun Yao, Yajun Li, Chenchen Wang, Xinrui Lv

  2011-09-01

  DOI:10.4208/cicp.150709.130410a

  39583 5103 pp. 180-204

• Solving Multi-Group Neutron Diffusion Eigenvalue Problem with Decoupling Residual Loss Function

  Shupei Yu, Qiaolin He, Shiquan Zhang, Qihong Yang, Yu Yang, Helin Gong

  2026-01-18

  DOI:10.4208/cicp.OA-2024-0176

  777 109 pp. 1231-1266

• Time-Lapse 3-D Seismic Wave Simulation via the Generalized Multiscale Finite Element Method

  Yongchae Cho, Richard L. Gibson, Hyunmin Kim, Mikhail Artemyev, Yalchin Efendiev

  2020-06-05

  DOI:10.4208/cicp.OA-2018-0086

  49162 4451 pp. 401-423

• Neural-Network-Augmented Empirical Interpolation Method for Field Reconstruction with Noise and Vibration Tolerance

  Han Li, Helin Gong, Chuanju Xu

  2026-01-03

  DOI:10.4208/cicp.OA-2024-0099

  1929 82 pp. 855-883