Search Results

• Fast Evaluation of the Caputo Fractional Derivative and Its Applications to Fractional Diffusion Equations

  Shidong Jiang, Jiwei Zhang, Qian Zhang & Zhimin Zhang

  2018-04-09

  52175 3391 Pages:650-678

• Parareal-Richardson Algorithm for Solving Nonlinear ODEs and PDEs

  Shulin Wu, Baochang Shi & Chengming Huang

  2009-06-01

  37431 4086 Pages:883-902

• A GPU-Accelerated Cartesian Grid Method for PDEs on Irregular Domain

  Liwei Tan, Minsheng Huang, Shuai Zhu, Pan Wang, Wenjun Ying

  2025-05-29

  8936 544 Pages:1250-1276

• 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

  42734 3244 Pages:1221-1240

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

  Shu-Lin Wu & Chengming Huang

  2018-10-11

  44419 3452 Pages:390-415

• Deep Learning-Based Reduced-Order Methods for Fast Transient Dynamics

  Martina Cracco, Giovanni Stabile, Andrea Lario, Armin Sheidani, Martin Larcher, Folco Casadei, Georgios Valsamos, Gianluigi Rozza

  2026-01-03

  1892 137 Pages:635-660

• 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

  5235 749 Pages:181-222

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

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

  2025-08-23

  6514 584 Pages:603-629

• Local Discontinuous Galerkin Methods for High-Order Time-Dependent Partial Differential Equations

  Yan Xu & Chi-Wang Shu

  2010-07-01

  42128 4813 Pages:1-46 Open-access

• A Rate of Convergence of Physics Informed Neural Networks for the Linear Second Order Elliptic PDEs

  Yuling Jiao, Yanming Lai, Dingwei Li, Xiliang Lu, Fengru Wang, Yang Wang, Jerry Zhijian Yang

  2022-03-30

  51988 3131 Pages:1272-1295

• Solving Allen-Cahn and Cahn-Hilliard Equations Using the Adaptive Physics Informed Neural Networks

  Colby L. Wight, Jia Zhao

  2021-01-13

  59168 3906 Pages:930-954

• Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

  Ameya D. Jagtap, George Em Karniadakis

  2020-11-18

  149394 6595 Pages:2002-2041

• Long-Time Integration of Nonlinear Wave Equations with Neural Operators

  Guanhang Lei, Zhen Lei, Lei Shi

  2026-01-18

  242 59 Pages:1137-1163

• An Efficient Reduced-Order Model Based on Dynamic Mode Decomposition for Parameterized Spatial High-Dimensional PDEs

  Yifan Lin, Xiang Sun, Jie Nie, Yuanhong Chen, Zhen Gao

  2025-09-02

  11746 904 Pages:575-602

• Learning Specialized Activation Functions for Physics-Informed Neural Networks

  Honghui Wang, Lu Lu, Shiji Song, Gao Huang

  2023-11-08

  34553 2896 Pages:869-906

• A Five-Point TENO Scheme with Adaptive Dissipation Based on a New Scale Sensor

  Haohan Huang, Tian Liang, Lin Fu

  2023-05-12

  36116 2926 Pages:1106-1131

• Nonlinear Reduced DNN Models for State Estimation

  Wolfgang Dahmen, Min Wang, Zhu Wang

  2022-07-06

  42845 3718 Pages:1-40

• Convergence Rate Analysis for Deep Ritz Method

  Chenguang Duan, Yuling Jiao, Yanming Lai, Dingwei Li, Xiliang Lu, Jerry Zhijian Yang

  2022-03-30

  58970 3389 Pages:1020-1048

• An Efficient Operator-Splitting Method for Noise Removal in Images

  D. Krishnan, P. Lin & X.-C. Tai

  2006-01-01

  39486 4020 Pages:847-858

• Structure-Preserving Numerical Methods for Stochastic Poisson Systems

  Jialin Hong, Jialin Ruan, Liying Sun, Lijin Wang

  2021-01-13

  47408 3382 Pages:802-830

• 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

  55176 3525 Pages:698-728

• Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains

  Ziqi Liu, Wei Cai, Zhi-Qin John Xu

  2020-11-18

  73856 3682 Pages:1970-2001

• Preface

  2020-11-18

  245 60 Pages:i-i

• Improved RBF Collocation Methods for Fourth Order Boundary Value Problems

  C. S. Chen, Andreas Karageorghis, Hui Zheng

  2020-05-06

  50394 3437 Pages:1530-1549

• A Nonlinear Elimination Preconditioner for Fully Coupled Space-Time Solution Algorithm with Applications to High-Rayleigh Number Thermal Convective Flow Problems

  Haijian Yang & Feng-Nan Hwang

  2019-04-28

  46149 3236 Pages:749-767

• Hopf Bifurcation and Time Periodic Orbits with pde2path – Algorithms and Applications

  Hannes Uecker

  2018-11-09

  48327 3454 Pages:812-852

• 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

  31843 2797 Pages:1133-1176