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• Generalization Error Analysis of Neural Networks with Gradient Based Regularization

  Lingfeng Li, Xue-Cheng Tai, Jiang Yang

  2022-10-28

  45808 3320 Pages:1007-1038

• Two Physics-Based Schwarz Preconditioners for Three-Temperature Radiation Diffusion Equations in High Dimensions

  Xiaoqiang Yue, Jianmeng He, Xiaowen Xu, Shi Shu, Libo Wang

  2022-09-29

  41787 3330 Pages:829-849

• A Holomorphic Operator Function Approach for the Transmission Eigenvalue Problem of Elastic Waves

  Yingxia Xi, Xia Ji

  2022-08-11

  301771 3371 Pages:524-546

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

  Xiaodong Feng, Li Zeng, Tao Zhou

  2022-08-11

  308979 3589 Pages:401-423

• Nonlinear Reduced DNN Models for State Estimation

  Wolfgang Dahmen, Min Wang, Zhu Wang

  2022-07-06

  42933 3767 Pages:1-40

• Integral Equation Method for a Non-Selfadjoint Steklov Eigenvalue Problem

  Yunyun Ma, Jiguang Sun

  2022-05-06

  45112 3293 Pages:1546-1560

• Convergence Rate Analysis for Deep Ritz Method

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

  2022-03-30

  59109 3453 Pages:1020-1048

• High-Order Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for Euler Equations with Gravitation on Unstructured Meshes

  Weijie Zhang, Yulong Xing, Yinhua Xia, Yan Xu

  2022-03-03

  47984 3244 Pages:771-815

• High Order Deep Neural Network for Solving High Frequency Partial Differential Equations

  Zhipeng Chang, Ke Li, Xiufen Zou, Xueshuang Xiang

  2022-01-27

  46266 3535 Pages:370-397

• High Order Finite Difference Hermite WENO Fixed-Point Fast Sweeping Method for Static Hamilton-Jacobi Equations

  Yupeng Ren, Yulong Xing, Jianxian Qiu

  2021-12-06

  47621 3923 Pages:154-187

• A Modified Adaptive Improved Mapped WENO Method

  Ruo Li, Wei Zhong

  2021-10-26

  46221 3263 Pages:1545-1588

• Examining Saddle Point Searches in the Context of Off-Lattice Kinetic Monte Carlo

  Jonathan Hicks, Timothy P. Schulze

  2021-07-01

  47892 3198 Pages:749-770

• High Order Discretely Well-Balanced Methods for Arbitrary Hydrostatic Atmospheres

  Jonas P. Berberich, Roger Käppeli, Praveen Chandrashekar, Christian Klingenberg

  2021-07-01

  49542 3298 Pages:666-708

• A WENO-Based Stochastic Galerkin Scheme for Ideal MHD Equations with Random Inputs

  Kailiang Wu, Dongbin Xiu, Xinghui Zhong

  2021-05-25

  49104 3204 Pages:423-447

• Dissipative and Conservative Local Discontinuous Galerkin Methods for the Fornberg-Whitham Type Equations

  Qian Zhang, Yan Xu, Chi-Wang Shu

  2021-05-25

  50983 3312 Pages:321-356

• Truncated $L_1$ Regularized Linear Regression: Theory and Algorithm

  Mingwei Dai, Shuyang Dai, Junjun Huang, Lican Kang, Xiliang Lu

  2021-04-30

  50095 4778 Pages:190-209

• A Mortar Spectral Element Method for Full-Potential Electronic Structure Calculations

  Yichen Guo, Lueling Jia, Huajie Chen, Huiyuan Li, Zhimin Zhang

  2021-03-24

  48361 3367 Pages:1541-1569

• An Adaptive Finite Element PML Method for the Open Cavity Scattering Problems

  Yanli Chen, Peijun Li, Xiaokai Yuan

  2021-03-24

  46145 3316 Pages:1505-1540

• A Highly Scalable Boundary Integral Equation and Walk-on-Spheres (BIE-WOS) Method for the Laplace Equation with Dirichlet Data

  Changhao Yan, Wei Cai, Xuan Zeng

  2021-03-24

  44964 3236 Pages:1446-1468

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

  Yulei Liao, Pingbing Ming

  2021-03-24

  53487 3558 Pages:1365-1384

• A Fast Time Splitting Finite Difference Approach to Gross–Pitaevskii Equations

  Marco Caliari, Simone Zuccher

  2021-03-24

  47941 3304 Pages:1336-1364

• A Decoupled Energy Stable Adaptive Finite Element Method for Cahn–Hilliard–Navier–Stokes Equations

  Yaoyao Chen, Yunqing Huang, Nianyu Yi

  2021-02-25

  48016 3478 Pages:1186-1212

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

  Colby L. Wight, Jia Zhao

  2021-01-13

  59545 3983 Pages:930-954

• A Nonlinear Finite Volume Scheme Preserving Maximum Principle for Diffusion Equations

  Jinjing Xu, Fei Zhao, Zhiqiang Sheng, Guangwei Yuan

  2021-01-13

  45865 3382 Pages:747-766

• Multi-Mesh-Scale Approximation of Thin Geophysical Mass Flows on Complex Topographies

  Yih-Chin Tai, Jeaniffer Vides, Boniface Nkonga, Chih-Yu Kuo

  2020-11-26

  46618 4291 Pages:148-185

• Multi-Scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains

  Bo Wang, Wenzhong Zhang, Wei Cai

  2020-11-18

  64547 3360 Pages:2139-2157

• 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

  74155 3747 Pages:1970-2001