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

  17 5 Pages: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

  17858 1214 Pages: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

  35658 2886 Pages: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

  9410 825 Pages:877-920 Open-access

• Opinion Dynamics of Sznajd Model on Small-World Network

  L. Guo, X. Cai

  2009-06-01

  39854 4178 Pages: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

  11903 807 Pages: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

  11887 914 Pages:315-352

• Computationally Efficient Fluid-Particle Dynamics Simulations of Arterial Systems

  Tejas S. Umbarkar, Clement Kleinstreuer

  2020-07-30

  40644 3034 Pages: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

  55420 3557 Pages:698-728

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

  Yulei Liao, Pingbing Ming

  2021-03-24

  53487 3558 Pages:1365-1384

• Dirichlet-Neumann Learning Algorithm for Solving Elliptic Interface Problems

  Qi Sun, Xuejun Xu, Haotian Yi

  2025-07-11

  5421 676 Pages: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

  9320 578 Pages: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

  50085 4589 Pages: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

  28537 2079 Pages: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

  46266 3535 Pages: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

  26429 2324 Pages:467-497

• Deep Unfitted Nitsche Method for Elliptic Interface Problems

  Hailong Guo, Xu Yang

  2022-03-30

  52735 3334 Pages: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

  32024 2860 Pages: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

  303892 3516 Pages:336-363

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

  L. Guo, X. Cai

  2010-07-01

  39610 4144 Pages: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

  36490 2925 Pages: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

  5368 890 Pages: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

  33593 2900 Pages: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

  39575 5093 Pages: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

  749 105 Pages: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

  49148 4443 Pages: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

  1900 77 Pages:855-883