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

  52310 3458 Pages:650-678

• 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

  2147 190 Pages:635-660

• 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

  42830 3286 Pages:1221-1240

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

  Shu-Lin Wu, Chengming Huang

  2018-10-11

  44507 3500 Pages:390-415

• Parareal-Richardson Algorithm for Solving Nonlinear ODEs and PDEs

  Shulin Wu, Baochang Shi, Chengming Huang

  2009-06-01

  37507 4127 Pages:883-902

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

  Guanhang Lei, Zhen Lei, Lei Shi

  2026-01-18

  784 143 Pages:1137-1163

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

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

  2025-08-23

  6666 629 Pages:603-629

• 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

  5370 894 Pages:181-222

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

  Yan Xu, Chi-Wang Shu

  2010-07-01

  42253 4903 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

  52176 3172 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

  59558 3987 Pages:930-954

• 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

  11911 969 Pages:575-602

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

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

  2025-05-29

  9078 580 Pages:1250-1276

• 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

  151358 6968 Pages:2002-2041

• Learning Specialized Activation Functions for Physics-Informed Neural Networks

  Honghui Wang, Lu Lu, Shiji Song, Gao Huang

  2023-11-08

  34818 2963 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

  36268 3052 Pages:1106-1131

• Nonlinear Reduced DNN Models for State Estimation

  Wolfgang Dahmen, Min Wang, Zhu Wang

  2022-07-06

  42938 3767 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

  59110 3456 Pages:1020-1048

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

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

  2006-01-01

  39576 4069 Pages:847-858

• Structure-Preserving Numerical Methods for Stochastic Poisson Systems

  Jialin Hong, Jialin Ruan, Liying Sun, Lijin Wang

  2021-01-13

  47547 3428 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

  55424 3559 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

  74175 3751 Pages:1970-2001

• Preface

  2020-11-18

  365 104 Pages:i-i

• Improved RBF Collocation Methods for Fourth Order Boundary Value Problems

  C. S. Chen, Andreas Karageorghis, Hui Zheng

  2020-05-06

  50527 3479 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

  46229 3269 Pages:749-767

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

  Hannes Uecker

  2018-11-09

  48470 3493 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

  32029 2861 Pages:1133-1176