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• Theory of the Frequency Principle for General Deep Neural Networks

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

  2021-08-31

  44541 3626 Pages:484-507

• Embedding Principle in Depth for the Loss Landscape Analysis of Deep Neural Networks

  Zhiwei Bai, Tao Luo, Zhi-Qin John Xu, Yaoyu Zhang

  2024-05-20

  21221 1862 Pages:350-389

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

  Yihe Liu, Xianmin Xu

  2025-02-11

  11075 963 Pages:63-95

• Unconditionally Maximum-Principle-Preserving Parametric Integrating Factor Two-Step Runge-Kutta Schemes for Parabolic Sine-Gordon Equations

  Hong Zhang, Xu Qian, Jun Xia, Songhe Song

  2023-01-09

  33305 3666 Pages:177-224

• An Integrated Quadratic Reconstruction for Finite Volume Schemes to Scalar Conservation Laws in Multiple Dimensions

  Li Chen, Ruo Li, Feng Yang

  2020-09-25

  39853 3475 Pages:491-517

• Stochastic Runge-Kutta Methods for Preserving Maximum Bound Principle of Semilinear Parabolic Equations. Part II: Sinc Quadrature Rule

  Yabing Sun, Weidong Zhao

  2025-02-11

  10901 893 Pages:176-206

• A New $\mathcal{L}1$-TFPM Scheme for the Singularly Perturbed Subdiffusion Equations

  Wang Kong, Zhongyi Huang

  2025-02-11

  11165 969 Pages:1-30

• Stochastic Runge-Kutta Methods for Preserving Maximum Bound Principle of Semilinear Parabolic Equations. Part I: Gaussian Quadrature Rule

  Yabing Sun, Weidong Zhao

  2024-05-20

  21538 1808 Pages:390-420

• A Survey of Optimal Control Problems Evolved on Riemannian Manifolds

  Li Deng, Xu Zhang

  2022-08-31

  34580 3113 Pages:351-382

• 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

  38201 3221 Pages:299-317

• Boundary Condition for Dislocation Dynamic Simulation in BCC Crystal

  Shuyang Dai, Fengru Wang, Yang Xiang, Jerry Zhijian Yang, Cheng Yuan

  2021-02-26

  41275 4279 Pages:175-194

• Optical Wave Turbulence: The Conformal Symmetry Transformations of Statistics of the Quantum Fluids of Light

  V. N. Grebenev

  2025-06-30

  262 20 Open-access

• Computational Imaging of Small-Amplitude Biperiodic Surfaces with Negative Index Material

  Yuliang Wang

  2025-02-11

  10951 980 Pages:148-175

• A Nonlinear Eigenvalue Problem Associated with the Sum-of-Rayleigh-Quotients Maximization

  Lei-Hong Zhang, Rui Chang

  2021-05-13

  42614 3871 Pages:313-335