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Solving high-dimensional partial differential equations using deep learning

Proceedings of the National Academy of Sciences - PNAS, 2018-08, Vol.115 (34), p.8505-8510

2018

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Phase Diagram of a Deep Potential Water Model

Physical review letters, 2021-06, Vol.126 (23), p.1-236001, Article 236001

2021

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Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations

Journal of nonlinear science, 2019-08, Vol.29 (4), p.1563-1619

2019

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DeePCG: Constructing coarse-grained models via deep neural networks

The Journal of chemical physics, 2018-07, Vol.149 (3), p.034101-034101

2018

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Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations

Communications in mathematics and statistics, 2017-12, Vol.5 (4), p.349-380

2017

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Deep Potential Molecular Dynamics: A Scalable Model with the Accuracy of Quantum Mechanics

Physical review letters, 2018-04, Vol.120 (14), p.143001-143001, Article 143001

2018

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The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems

Communications in mathematics and statistics, 2018-03, Vol.6 (1), p.1-12

2018

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A Proposal on Machine Learning via Dynamical Systems

Communications in mathematics and statistics, 2017-03, Vol.5 (1), p.1-11

E, Weinan

2017

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A mean-field optimal control formulation of deep learning

Research in the mathematical sciences, 2019-01, Vol.6 (1), p.1-41, Article 10

2019

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The Barron Space and the Flow-Induced Function Spaces for Neural Network Models

Constructive approximation, 2022-02, Vol.55 (1), p.369-406

2022

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Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning

Nonlinearity, 2022-01, Vol.35 (1), p.278-310

2022

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DP-GEN: A concurrent learning platform for the generation of reliable deep learning based potential energy models

Computer physics communications, 2020-08, Vol.253 (C), p.107206, Article 107206

2020

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A comparative analysis of optimization and generalization properties of two-layer neural network and random feature models under gradient descent dynamics

Science China. Mathematics, 2020-07, Vol.63 (7), p.1235-1258

2020

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Machine learning from a continuous viewpoint, I

Science China. Mathematics, 2020-11, Vol.63 (11), p.2233-2266

2020

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DeePKS: A Comprehensive Data-Driven Approach toward Chemically Accurate Density Functional Theory

Journal of chemical theory and computation, 2021-01, Vol.17 (1), p.170-181

2021

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Solving many-electron Schrödinger equation using deep neural networks

Journal of computational physics, 2019-12, Vol.399, p.108929, Article 108929

2019

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Ground State Energy Functional with Hartree–Fock Efficiency and Chemical Accuracy

The journal of physical chemistry. A, Molecules, spectroscopy, kinetics, environment, & general theory, 2020-09, Vol.124 (35), p.7155-7165

2020

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Exponential convergence of the deep neural network approximation for analytic functions

Science China. Mathematics, 2018-10, Vol.61 (10), p.1733-1740

2018

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Representation formulas and pointwise properties for Barron functions

Calculus of variations and partial differential equations, 2022-04, Vol.61 (2), Article 46

2022

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On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations

Journal of scientific computing, 2019-06, Vol.79 (3), p.1534-1571

2019

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Active learning of uniformly accurate interatomic potentials for materials simulation

Physical review materials, 2019-02, Vol.3 (2), Article 023804

2019

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Reinforced dynamics for enhanced sampling in large atomic and molecular systems

The Journal of chemical physics, 2018-03, Vol.148 (12), p.124113-124113

2018

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DeFine: deep convolutional neural networks accurately quantify intensities of transcription factor-DNA binding and facilitate evaluation of functional non-coding variants

Nucleic acids research, 2018-06, Vol.46 (11), p.e69

2018

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Transition-path theory and path-finding algorithms for the study of rare events

Annual review of physical chemistry, 2010-01, Vol.61 (1), p.391-420

2010

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Uniformly accurate machine learning-based hydrodynamic models for kinetic equations

Proceedings of the National Academy of Sciences - PNAS, 2019-10, Vol.116 (44), p.21983-21991

2019

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Solving high-dimensional partial differential equations using deep learning

Phase Diagram of a Deep Potential Water Model

Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations

DeePCG: Constructing coarse-grained models via deep neural networks

Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations

Deep Potential Molecular Dynamics: A Scalable Model with the Accuracy of Quantum Mechanics

The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems

A Proposal on Machine Learning via Dynamical Systems

A mean-field optimal control formulation of deep learning

The Barron Space and the Flow-Induced Function Spaces for Neural Network Models

Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning

DP-GEN: A concurrent learning platform for the generation of reliable deep learning based potential energy models

A comparative analysis of optimization and generalization properties of two-layer neural network and random feature models under gradient descent dynamics

Machine learning from a continuous viewpoint, I

DeePKS: A Comprehensive Data-Driven Approach toward Chemically Accurate Density Functional Theory

Solving many-electron Schrödinger equation using deep neural networks

Ground State Energy Functional with Hartree–Fock Efficiency and Chemical Accuracy

Exponential convergence of the deep neural network approximation for analytic functions

Representation formulas and pointwise properties for Barron functions

On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations

Active learning of uniformly accurate interatomic potentials for materials simulation

Reinforced dynamics for enhanced sampling in large atomic and molecular systems

DeFine: deep convolutional neural networks accurately quantify intensities of transcription factor-DNA binding and facilitate evaluation of functional non-coding variants

Transition-path theory and path-finding algorithms for the study of rare events

Uniformly accurate machine learning-based hydrodynamic models for kinetic equations

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