Search Results

• Identification of Corrupted Data via $k$-Means Clustering for Function Approximation

  Jun Hou, Yeonjong Shin, Dongbin Xiu

  2021-02-26

  40864 4131 Pages:81-107

• A Two-Level Simultaneous Orthogonal Matching Pursuit Algorithm for Simultaneous Sparse Approximation Problems

  Nian Shao, Rui Zhang, Jie Sun, Wenbin Chen

  2023-10-26

  27114 2626 Pages:758-775

• An $L^2$ Analysis of Reinforcement Learning in High Dimensions with Kernel and Neural Network Approximation

  Jihao Long, Jiequn Han, Weinan E

  2022-05-30

  40073 3207 Pages:191-220

• Solving Time-Dependent Parametric PDEs by Multiclass Classification-Based Reduced Order Model

  Chen Cui, Kai Jiang, Shi Shu

  2023-01-09

  34254 3790 Pages:13-40

• Deep Ritz Methods for Laplace Equations with Dirichlet Boundary Condition

  Chenguang Duan, Yuling Jiao, Yanming Lai, Xiliang Lu, Qimeng Quan, Jerry Zhijian Yang

  2022-11-07

  295290 3160 Pages:761-791

• Mathematical and Numerical Analysis to Shrinking-Dimer Saddle Dynamics with Local Lipschitz Conditions

  Lei Zhang, Pingwen Zhang, Xiangcheng Zheng

  2023-01-09

  33554 3370 Pages:157-176

• On the Optimal Order Approximation of the Partition of Unity Finite Element Method

  Yunqing Huang, Shangyou Zhang

  2024-05-20

  23906 2172 Pages:221-233

• Efficient Two-Dimensional Randomized Progressive Iterative Approximation for Large-Scale B-Spline Fitting

  Chengzhi Liu, Nian-Ci Wu, Juncheng Li

  2026-05-01

  338 51 Pages:556-575

• A Variational Discretization Method for Mean Curvature Flows by the Onsager Principle

  Yihe Liu, Xianmin Xu

  2025-02-11

  11481 1175 Pages:63-95

• pETNNs: Partial Evolutionary Tensor Neural Networks for Solving Time-Dependent Partial Differential Equations

  Tunan Kao, He Zhang, Lei Zhang, Jin Zhao

  2025-09-30

  19532 549 Pages:862-891

• Multipliers Correction Methods for Optimization Problems over the Stiefel Manifold

  Lei Wang, Bin Gao, Xin Liu

  2021-08-31

  45003 3741 Pages:508-531

• General Tikhonov Regularization with Applications in Geoscience

  Yanfei Wang, Alexander S. Leonov, Dmitry V. Lukyanenko, Anatoly G. Yagola

  2020-04-30

  62842 5263 Pages:53-85

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

  Xiaokai Yuan, Gang Bao, Peijun Li

  2020-07-01

  43980 3972 Pages:316-345

• On the Banach Spaces Associated with Multi-Layer ReLU Networks: Function Representation, Approximation Theory and Gradient Descent Dynamics

  Weinan E, Stephan Wojtowytsch

  2020-09-25

  43957 3853 Pages:387-440

• Towards a Mathematical Understanding of Neural Network-Based Machine Learning: What We Know and What We Don't

  Weinan E, Chao Ma, Lei Wu, Stephan Wojtowytsch

  2020-12-31

  50421 4558 Pages:561-615

• Super-Resolution Inversion of Non-Stationary Seismic Traces

  Jinghuai Gao, Hongling Chen, Lingling Wang, Bing Zhang

  2021-02-26

  40917 4269 Pages:131-161

• Multi-Layer Hierarchical Structures

  Jianlin Xia

  2021-05-13

  43656 3802 Pages:263-296

• Combined Second and Fourth-Order PDEs Model and Associated Variational Problems for Geometric Images Inpainting and Denoising

  Anis Theljani, Zakaria Belhachmi, Moez Kallel, Maher Moakher

  2021-11-29

  38685 3507 Pages:652-679

• Solving the $k$-Sparse Eigenvalue Problem with Reinforcement Learning

  Li Zhou, Lihao Yan, Mark A. Caprio, Weiguo Gao, Chao Yang

  2021-11-29

  40881 3496 Pages:697-723

• A Saturation-Component Based Fuzzy Mumford-Shah Model for Color Image Segmentation

  Wei Wang, Caifei Li, Michael K. Ng

  2021-11-29

  39037 3551 Pages:724-747

• A Holomorphic Operator Function Approach for the Laplace Eigenvalue Problem Using Discontinuous Galerkin Method

  Yingxia Xi, Xia Ji

  2021-11-29

  38766 3364 Pages:776-792

• Implicit Bias in Understanding Deep Learning for Solving PDEs Beyond Ritz-Galerkin Method

  Jihong Wang, Zhi-Qin John Xu, Jiwei Zhang, Yaoyu Zhang

  2022-05-30

  38447 3288 Pages:299-317

• A Splitting Hamiltonian Monte Carlo Method for Efficient Sampling

  Lei Li, Lin Liu, Yuzhou Peng

  2023-01-09

  34100 3941 Pages:41-73

• Review of Entropy Stable Discontinuous Galerkin Methods for Systems of Conservation Laws on Unstructured Simplex Meshes

  Tianheng Chen, Chi-Wang Shu

  2020-04-30

  90698 5969 Pages:1-52

• Asymptotic Expansion Regularization for Inverse Source Problems in Two-Dimensional Singularly Perturbed Nonlinear Parabolic PDEs

  Dmitrii Chaikovskii, Aleksei Liubavin, Ye Zhang

  2023-10-26

  27463 2521 Pages:721-757

• A $C^1$-Conforming Gauss Collocation Method for Elliptic Equations and Superconvergence Analysis Over Rectangular Meshes

  Waixiang Cao, Lueling Jia, Zhimin Zhang

  2024-05-20

  20684 1839 Pages:320-349

• Determination of Source Terms in Diffusion and Wave Equations by Observations After Incidents: Uniqueness and Stability

  Jin Cheng, Shuai Lu, Masahiro Yamamoto

  2023-02-14

  31983 3076 Pages:381-418