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Zhi-Qin John Xu

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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”

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

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MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs

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

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Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks

Journal Article

Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks

Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1746–1767

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

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

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Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains

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

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

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

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Theory of the Frequency Principle for General Deep Neural Networks

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

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Embedding Principle: A Hierarchical Structure of Loss Landscape of Deep Neural Networks

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

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

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

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Phase Diagram of Initial Condensation for Two-Layer Neural Networks

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

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Loss Jump During Loss Switch in Solving PDEs with Neural Networks

Journal Article

Loss Jump During Loss Switch in Solving PDEs with Neural Networks

Communications in Computational Physics, Vol. 36 (2024), Iss. 4 : pp. 1090–1112

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Laplace-fPINNs: Laplace-Based Fractional Physics-Informed Neural Networks for Solving Forward and Inverse Problems of a Time Fractional Equation

Journal Article

Laplace-fPINNs: Laplace-Based Fractional Physics-Informed Neural Networks for Solving Forward and Inverse Problems of a Time Fractional Equation

East Asian Journal on Applied Mathematics, Vol. 14 (2024), Iss. 4 : pp. 657–674

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