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

  52311 3460 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

  2152 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 3287 Pages:1221-1240

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

  Shu-Lin Wu, Chengming Huang

  2018-10-11

  44510 3502 Pages:390-415

• Parareal-Richardson Algorithm for Solving Nonlinear ODEs and PDEs

  Shulin Wu, Baochang Shi, Chengming Huang

  2009-06-01

  37509 4128 Pages:883-902

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

  Guanhang Lei, Zhen Lei, Lei Shi

  2026-01-18

  791 145 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

  6671 631 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

  5373 896 Pages:181-222

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

  Yan Xu, Chi-Wang Shu

  2010-07-01

  42255 4906 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

  52180 3175 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

  59570 3990 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

  11913 970 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

  9080 581 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

  151476 6984 Pages:2002-2041

• Learning Specialized Activation Functions for Physics-Informed Neural Networks

  Honghui Wang, Lu Lu, Shiji Song, Gao Huang

  2023-11-08

  34824 2964 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

  36271 3053 Pages:1106-1131

• Nonlinear Reduced DNN Models for State Estimation

  Wolfgang Dahmen, Min Wang, Zhu Wang

  2022-07-06

  42940 3769 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

  59115 3460 Pages:1020-1048

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

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

  2006-01-01

  39578 4071 Pages:847-858

• Structure-Preserving Numerical Methods for Stochastic Poisson Systems

  Jialin Hong, Jialin Ruan, Liying Sun, Lijin Wang

  2021-01-13

  47551 3430 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

  55430 3561 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

  74193 3753 Pages:1970-2001

• Preface

  2020-11-18

  378 105 Pages:i-i

• Improved RBF Collocation Methods for Fourth Order Boundary Value Problems

  C. S. Chen, Andreas Karageorghis, Hui Zheng

  2020-05-06

  50533 3480 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

  46231 3271 Pages:749-767

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

  Hannes Uecker

  2018-11-09

  48476 3496 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

  32039 2870 Pages:1133-1176