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• An Augmented Lagrangian Deep Learning Method for Variational Problems with Essential Boundary Conditions

  Jianguo Huang, Haoqin Wang, Tao Zhou

  2022-03-03

  50575 3314 Pages:966-986

• An Enhanced Finite Element Method for a Class of Variational Problems Exhibiting the Lavrentiev Gap Phenomenon

  Xiaobing Feng & Stefan Schnake

  2018-09-17

  45235 3166 Pages:576-592

• Deep Learning-Based Computational Method for Soft Matter Dynamics: Deep Onsager-Machlup Method

  Zhihao Li, Boyi Zou, Haiqin Wang, Jian Su, Dong Wang, Xinpeng Xu

  2025-09-02

  11749 752 Pages:353-382

• Generalization Error Analysis of Neural Networks with Gradient Based Regularization

  Lingfeng Li, Xue-Cheng Tai, Jiang Yang

  2022-10-28

  45663 3276 Pages:1007-1038

• A Variational Neural Network Approach for Glacier Modelling with Nonlinear Rheology

  Tiangang Cui, Zhongjian Wang, Zhiwen Zhang

  2023-11-08

  30842 2583 Pages:934-954

• VAE-KRnet and Its Applications to Variational Bayes

  Xiaoliang Wan, Shuangqing Wei

  2022-03-30

  52262 3243 Pages:1049-1082

• Dirichlet-Neumann Learning Algorithm for Solving Elliptic Interface Problems

  Qi Sun, Xuejun Xu, Haotian Yi

  2025-07-11

  5279 579 Pages:248-284

• A Multi-Scale DNN Algorithm for Nonlinear Elliptic Equations with Multiple Scales

  Xi-An Li, Zhi-Qin John Xu, Lei Zhang

  2020-11-18

  67253 3664 Pages:1886-1906

• Three-Phase Model of Visco-Elastic Incompressible Fluid Flow and Its Computational Implementation

  Shixin Xu, Mark Alber & Zhiliang Xu

  2018-10-11

  48639 3413 Pages:586-624

• Pressure-Correction Projection FEM for Time-Dependent Natural Convection Problem

  Jilian Wu, Xinlong Feng & Fei Liu

  2018-04-09

  43443 3181 Pages:1090-1117

• Existence and Uniqueness of the Weak Solution of the Space-Time Fractional Diffusion Equation and a Spectral Method Approximation

  Xianjuan Li & Chuanju Xu

  2010-08-01

  46296 4816 Pages:1016-1051

• 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

  307095 3600 Pages:299-335

• VPVnet: A Velocity-Pressure-Vorticity Neural Network Method for the Stokes’ Equations under Reduced Regularity

  Yujie Liu, Chao Yang

  2022-03-03

  45524 3235 Pages:739-770

• Physics-Constrained, Data-Driven Discovery of Coarse-Grained Dynamics

  Lukas Felsberger & Phaedon-Stelios Koutsourelakis

  2019-01-10

  48659 5379 Pages:1259-1301

• Stability and Conservation Properties of Collocated Constraints in Immersogeometric Fluid-Thin Structure Interaction Analysis

  David Kamensky, John A. Evans & Ming-Chen Hsu

  2020-07-31

  38542 3102 Pages:1147-1180

• Extension of the High-Order Space-Time Discontinuous Galerkin Cell Vertex Scheme to Solve Time Dependent Diffusion Equations

  Shuangzhang Tu, Gordon W. Skelton & Qing Pang

  2012-11-01

  38646 4041 Pages:1503-1524

• Geometric Evolution Laws for Thin Crystalline Films: Modeling and Numerics

  Bo Li, John Lowengrub, Andreas Rätz & Axel Voigt

  2009-06-01

  42000 4765 Pages:433-482 Open-access

• Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions

  Yulei Liao, Pingbing Ming

  2021-03-24

  53300 3485 Pages:1365-1384