Search Results

• 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

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

  Peter Popov, Yalchin Efendiev, Guan Qin

  2009-06-01

  38837 4685 Pages:162-184

• A Model-Data Asymptotic-Preserving Neural Network Method Based on Micro-Macro Decomposition for Gray Radiative Transfer Equations

  Hongyan Li, Song Jiang, Wenjun Sun, Liwei Xu, Guanyu Zhou

  2024-06-14

  36825 1981 Pages:1155-1193

• 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

  86781 4378 Pages:1746-1767

• 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

  15993 1215 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

  34258 2837 Pages:392-417

• Asymptotic-Preserving Neural Networks for Multiscale Kinetic Equations

  Shi Jin, Zheng Ma, Keke Wu

  2024-04-10

  25509 2191 Pages:693-723

• Towards the Efficient Calculation of Quantity of Interest from Steady Euler Equations II: A CNNs-Based Automatic Implementation

  Jingfeng Wang, Guanghui Hu

  2026-01-03

  1931 83 Pages:884-918

• 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

• 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

  35603 2926 Pages:813-836

• Scale-Decomposed Physics-Informed Neural Networks for Singular Perturbation Problems

  Lei Zhang, Guowei He

  2026-01-18

  1048 235 Pages:1267-1298

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

  Haoxiang Huang, Vigor Yang, Yingjie Liu

  2023-11-08

  77237 3709 Pages:907-933

• 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

• Generalization Error in the Deep Ritz Method with Smooth Activation Functions

  Janne Siipola

  2024-04-10

  24366 2439 Pages:761-815 Open-access

• Deep Network Approximation Characterized by Number of Neurons

  Zuowei Shen, Haizhao Yang, Shijun Zhang

  2020-11-18

  69198 3704 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

  48140 3150 Pages:820-850

• Transitions States of Stochastic Chemical Kinetic Systems

  Jun Du, Di Liu

  2020-12-02

  45502 3161 Pages:606-627

• An Efficient Iterative Method for the Formulation of Flow Networks

  Wei Hu, Dong Wang, Xiao-Ping Wang

  2022-05-06

  49671 3410 Pages:1317-1340

• Nonlinear Reduced DNN Models for State Estimation

  Wolfgang Dahmen, Min Wang, Zhu Wang

  2022-07-06

  42940 3769 Pages:1-40

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

  Chao Ma, Jianchun Wang, Weinan E

  2018-12-08

  59474 5372 Pages:947-962 Open-access

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

  Carlos Michelen Strofer, Jin-Long Wu, Heng Xiao, Eric Paterson

  2018-11-09

  66837 6245 Pages:625-650 Open-access

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

  Shamsulhaq Basir

  2023-06-06

  41856 3030 Pages:1240-1269

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

  Taeyoung Kim, Myungjoo Kang

  2025-09-02

  12321 905 Pages:420-456

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

  Jianguo Huang, Haohao Wu, Tao Zhou

  2026-02-15

  4083 195 Pages:553-577

• 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

  29083 2496 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

  29903 2823 Pages:1-37

• Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank

  Tao Tang, Jiang Yang, Yuxiang Zhao, Quanhui Zhu

  2026-03-16

  399 29 Pages:61-87