Search Results

• 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

  147761 6053 Pages:2002-2041

• Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks

  Zhi-Qin John Xu, Yaoyu Zhang, Tao Luo, Yanyang Xiao, Zheng Ma

  2020-11-18

  85482 4069 Pages:1746-1767

• Multiscale Modeling and Simulations of Flows in Naturally Fractured Karst Reservoirs

  Peter Popov, Yalchin Efendiev & Guan Qin

  2009-06-01

  38674 4554 Pages:162-184

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

  Colby L. Wight, Jia Zhao

  2021-01-13

  58901 3820 Pages:930-954

• Learning Specialized Activation Functions for Physics-Informed Neural Networks

  Honghui Wang, Lu Lu, Shiji Song, Gao Huang

  2023-11-08

  34363 2783 Pages:869-906

• A Rate of Convergence of Weak Adversarial Neural Networks for the Second Order Parabolic PDEs

  Yuling Jiao, Jerry Zhijian Yang, Cheng Yuan, Junyu Zhou

  2023-10-07

  35332 2836 Pages:813-836

• Convergence Analysis for Over-Parameterized Deep Learning

  Yuling Jiao, Xiliang Lu, Peiying Wu, Jerry Zhijian Yang

  2024-07-29

  157 147 Pages:71-103

• Time Integration Schemes Based on Neural Networks for Solving Partial Differential Equations on Coarse Grids

  Xinxin Yan, Zhideng Zhou, Xiaohan Cheng, Xiaolei Yang

  2024-12-02

  201 54 Pages:1262-1306

• Learning Invariant Representation of Multiscale Hyperelastic Constitutive Law from Sparse Experimental Data

  Rui He, Junzhi Cui, Zihao Yang, Jieqiong Zhang, Xiaofei Guan

  2023-09-04

  34022 2764 Pages:392-417

• Convergence Rate Analysis for Deep Ritz Method

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

  2022-03-30

  58803 3318 Pages:1020-1048

• Neural Networks with Local Converging Inputs (NNLCI) for Solving Conservation Laws, Part II: 2D Problems

  Haoxiang Huang, Vigor Yang, Yingjie Liu

  2023-11-08

  76945 3630 Pages:907-933

• Model Reduction with Memory and the Machine Learning of Dynamical Systems

  Chao Ma, Jianchun Wang & Weinan E

  2018-12-08

  59155 5193 Pages:947-962 Open-access

• Transitions States of Stochastic Chemical Kinetic Systems

  Jun Du, Di Liu

  2020-12-02

  45303 3110 Pages:606-627

• Data-Driven, Physics-Based Feature Extraction from Fluid Flow Fields Using Convolutional Neural Networks

  Carlos Michelén Ströfer, Jin-Long Wu, Heng Xiao & Eric Paterson

  2018-11-09

  66513 6097 Pages:625-650 Open-access

• Deep Network Approximation Characterized by Number of Neurons

  Zuowei Shen, Haizhao Yang, Shijun Zhang

  2020-11-18

  68719 3581 Pages:1768-1811

• An Understanding of the Physical Solutions and the Blow-up Phenomenon for Nonlinear Noisy Leaky Integrate and Fire Neuronal Models

  María J. Cáceres, Alejandro Ramos-Lora

  2021-07-01

  47973 3088 Pages:820-850

• An Efficient Iterative Method for the Formulation of Flow Networks

  Wei Hu, Dong Wang, Xiao-Ping Wang

  2022-05-06

  49474 3343 Pages:1317-1340

• Nonlinear Reduced DNN Models for State Estimation

  Wolfgang Dahmen, Min Wang, Zhu Wang

  2022-07-06

  42748 3674 Pages:1-40

• A Spectral Method for a Fokker-Planck Equation in Neuroscience with Applications in Neuron Networks with Learning Rules

  Pei Zhang, Yanli Wang, Zhennan Zhou

  2024-01-31

  28862 2368 Pages:70-106

• Splitting Physics-Informed Neural Networks for Inferring the Dynamics of Integer- and Fractional-Order Neuron Models

  Simin Shekarpaz, Fanhai Zeng, George Karniadakis

  2024-01-31

  29624 2647 Pages:1-37

• Approximating Numerical Fluxes Using Fourier Neural Operators for Hyperbolic Conservation Laws

  Taeyoung Kim, Myungjoo Kang

  2025-09-02

  204 76 Pages:420-456

• 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

  152 68 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

  35379 2818 Pages:290-317

• Investigating and Mitigating Failure Modes in Physics-Informed Neural Networks (PINNs)

  Shamsulhaq Basir

  2023-06-06

  41484 2933 Pages:1240-1269

• Adaptive Neural Network Basis Methods for Partial Differential Equations with Low-Regular Solutions

  Jianguo Huang, Haohao Wu, Tao Zhou

  2025-11-28

  913 40 Pages:553-577

• Preface

  2020-11-18

  119 47 Pages:i-i

• Finite Neuron Method and Convergence Analysis

  Jinchao Xu

  2020-11-18

  70207 3742 Pages:1707-1745