Zhi-Qin John Xu
Results
Journal Article
A Correction and Comments on “Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains CiCP, 28 (5): 1970–2001, 2020”
Communications in Computational Physics, Vol. 33 (2023), Iss. 5 : pp. 1509–1513
Journal Article
MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs
Communications in Computational Physics, Vol. 32 (2022), Iss. 2 : pp. 299–335
Journal Article
Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1746–1767
Journal Article
A Multi-Scale DNN Algorithm for Nonlinear Elliptic Equations with Multiple Scales
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1886–1906
Journal Article
Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1970–2001
Journal Article
Implicit Bias in Understanding Deep Learning for Solving PDEs Beyond Ritz-Galerkin Method
CSIAM Transactions on Applied Mathematics, Vol. 3 (2022), Iss. 2 : pp. 299–317
Journal Article
Theory of the Frequency Principle for General Deep Neural Networks
CSIAM Transactions on Applied Mathematics, Vol. 2 (2021), Iss. 3 : pp. 484–507
Journal Article
Embedding Principle: A Hierarchical Structure of Loss Landscape of Deep Neural Networks
Journal of Machine Learning, Vol. 1 (2022), Iss. 1 : pp. 60–113
Journal Article
Embedding Principle in Depth for the Loss Landscape Analysis of Deep Neural Networks
CSIAM Transactions on Applied Mathematics, Vol. 5 (2024), Iss. 2 : pp. 350–389
Journal Article
Phase Diagram of Initial Condensation for Two-Layer Neural Networks
CSIAM Transactions on Applied Mathematics, Vol. 5 (2024), Iss. 3 : pp. 448–514