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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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Machine Learning and Computational Mathematics

Journal Article

Machine Learning and Computational Mathematics

Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1639–1670

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Model Reduction with Memory and the Machine Learning of Dynamical Systems

Journal Article

Model Reduction with Memory and the Machine Learning of Dynamical Systems

Communications in Computational Physics, Vol. 25 (2019), Iss. 4 : pp. 947–962

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Deep Potential: A General Representation of a Many-Body Potential Energy Surface

Journal Article

Deep Potential: A General Representation of a Many-Body Potential Energy Surface

Communications in Computational Physics, Vol. 23 (2018), Iss. 3 : pp. 629–639

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Optimization-Based String Method for Finding Minimum Energy Path

Journal Article

Optimization-Based String Method for Finding Minimum Energy Path

Communications in Computational Physics, Vol. 14 (2013), Iss. 2 : pp. 265–275

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Effectiveness of Implicit Methods for Stiff Stochastic Differential Equations

Journal Article

Effectiveness of Implicit Methods for Stiff Stochastic Differential Equations

Communications in Computational Physics, Vol. 3 (2008), Iss. 2 : pp. 295–307

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Sequential Multiscale Modeling Using Sparse Representation

Journal Article

Sequential Multiscale Modeling Using Sparse Representation

Communications in Computational Physics, Vol. 4 (2008), Iss. 5 : pp. 1025–1033

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

Journal Article

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

CSIAM Transactions on Applied Mathematics, Vol. 3 (2022), Iss. 2 : pp. 191–220

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

Journal Article

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

CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 3 : pp. 387–440

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

Journal Article

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

CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 4 : pp. 561–615

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The Random Feature Method for Time-Dependent Problems

Journal Article

The Random Feature Method for Time-Dependent Problems

East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 3 : pp. 435–463

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DeePN$^2$: A Deep Learning-Based Non-Newtonian Hydrodynamic Model

Journal Article

DeePN$^2$: A Deep Learning-Based Non-Newtonian Hydrodynamic Model

Journal of Machine Learning, Vol. 1 (2022), Iss. 1 : pp. 114–140

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