Search Results

• Machine Learning and Computational Mathematics

  Weinan E

  2020-11-18

  88485 4276 Pages:1639-1670

• Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learning

  Yufei Wang, Ziju Shen, Zichao Long, Bin Dong

  2020-11-18

  62322 3419 Pages:2158-2179

• Finding the Origin of Noise Transients in LIGO Data with Machine Learning

  Marco Cavaglià, Kai Staats & Teerth Gill

  2018-12-08

  56618 4744 Pages:963-987 Open-access

• A Data-Driven Scale-Invariant Weighted Compact Nonlinear Scheme for Hyperbolic Conservation Laws

  Zixuan Zhang, Yidao Dong, Yuanyang Zou, Hao Zhang, Xiaogang Deng

  2024-05-06

  28295 2001 Pages:1120-1154

• A Data-Driven Random Subfeature Ensemble Learning Algorithm for Weather Forecasting

  Chen Yu, Haochen Li, Jiangjiang Xia, Hanqiuzi Wen, Pingwen Zhang

  2020-08-27

  50654 3287 Pages:1305-1320

• Data Generation-Based Operator Learning for Solving Partial Differential Equations on Unbounded Domains

  Jihong Wang, Xin Wang, Jing Li, Bin Liu

  2025-05-29

  194 50 Pages:1383-1416

• A Consensus-Based Global Optimization Method with Adaptive Momentum Estimation

  Jingrun Chen, Shi Jin, Liyao Lyu

  2022-03-30

  47006 2985 Pages:1296-1316

• 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

  54997 3468 Pages:698-728

• Newton’s Method and Its Hybrid with Machine Learning for Navier-Stokes Darcy Models Discretized by Mixed Element Methods

  Jianguo Huang, Hui Peng, Haohao Wu

  2025-01-22

  187 97 Pages:30-60

• Physically Guided Neural Network Based on Transfer Learning (TL-PGNN) for Hypersonic Heat Flux Prediction

  Biao Chen, Jifa Zhang, Shuai Zhang, Xiaoxiao Song, Yao Zheng

  2024-10-09

  181 59 Pages:651-672

• 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

• Solving Time Dependent Fokker-Planck Equations via Temporal Normalizing Flow

  Xiaodong Feng, Li Zeng, Tao Zhou

  2022-08-11

  308724 3524 Pages:401-423

• An Efficient Neural-Network and Finite-Difference Hybrid Method for Elliptic Interface Problems with Applications

  Wei-Fan Hu, Te-Sheng Lin, Yu-Hau Tseng, Ming-Chih Lai

  2023-05-12

  36233 2866 Pages:1090-1105

• A Data-Driven Reconstruction for Unstructured Finite Volume Method on Multi-Dimensional Compressible Flows

  Jayeon Joo, Dongseok Kim, Hojun You, Chongam Kim

  2024-12-02

  200 48 Pages:1307-1338

• 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

• MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs

  Lulu Zhang, Tao Luo, Yaoyu Zhang, Weinan E, Zhi-Qin John Xu, Zheng Ma

  2022-08-11

  306975 3553 Pages:299-335

• Adaptive Interface-PINNs (AdaI-PINNs): An Efficient Physics-Informed Neural Networks Framework for Interface Problems

  Sumanta Roy, Chandrasekhar Annavarapu, Pratanu Roy, Antareep Kumar Sarma

  2025-09-02

  431 93 Pages:603-622

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

  Taeyoung Kim, Myungjoo Kang

  2025-09-02

  204 76 Pages:420-456

• Preface

  2020-11-18

  119 47 Pages:i-i

• Butterfly-Net: Optimal Function Representation Based on Convolutional Neural Networks

  Yingzhou Li, Xiuyuan Cheng, Jianfeng Lu

  2020-11-18

  63549 3432 Pages:1838-1885

• Enforcing Imprecise Constraints on Generative Adversarial Networks for Emulating Physical Systems

  Yang Zeng, Jin-Long Wu, Heng Xiao

  2021-07-01

  49181 3239 Pages:635-665

• Continuous-Variable Deep Quantum Neural Networks for Flexible Learning of Structured Classical Information

  Jasvith Raj Basani, Aranya Bhattacherjee

  2021-08-10

  46112 2967 Pages:1216-1231

• 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

  31686 2665 Pages:1133-1176

• 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

• High-Dimensional Nonlinear Multi-Fidelity Model with Gradient-Free Active Subspace Method

  Bangde Liu, Guang Lin

  2020-11-18

  62412 3326 Pages:1937-1969

• Generalization Error Analysis of Neural Networks with Gradient Based Regularization

  Lingfeng Li, Xue-Cheng Tai, Jiang Yang

  2022-10-28

  45537 3242 Pages:1007-1038

• 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