PFNN: A penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries

Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

(2020) Maziar Raissi et al.   SCIENCE

Weak adversarial networks for high-dimensional partial differential equations

(2020) Yaohua Zang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

(2019) Christian Beck et al.   JOURNAL OF NONLINEAR SCIENCE

BCR-Net: A neural network based on the nonstandard wavelet form

(2019) Yuwei Fan et al.   JOURNAL OF COMPUTATIONAL PHYSICS

MgNet: A unified framework of multigrid and convolutional neural network

(2019) Juncai He et al.   Science China-Mathematics

PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network

(2019) Zichao Long et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Recent Trends in Deep Learning Based Natural Language Processing [Review Article]

(2018) Tom Young et al.   IEEE Computational Intelligence Magazine

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

(2018) Linfeng Zhang et al.   PHYSICAL REVIEW LETTERS

Turbulence Modeling in the Age of Data

(2018) Karthik Duraisamy et al.   Annual Review of Fluid Mechanics

DGM: A deep learning algorithm for solving partial differential equations

(2018) Justin Sirignano et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A unified deep artificial neural network approach to partial differential equations in complex geometries

(2018) Jens Berg et al.   NEUROCOMPUTING

Solving high-dimensional partial differential equations using deep learning

(2018) Jiequn Han et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

(2018) M. Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

(2016) Julia Ling et al.   JOURNAL OF FLUID MECHANICS

Understanding machine-learned density functionals

(2015) Li Li et al.   INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY

Deep learning

(2015) Yann LeCun et al.   NATURE

Deep learning in neural networks: An overview

(2015) Jürgen Schmidhuber   NEURAL NETWORKS

Automated design parameter selection for neural networks solving coupled partial differential equations with discontinuities

(2012) Kevin Stanley McFall   JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS

Artificial Neural Network Method for Solution of Boundary Value Problems With Exact Satisfaction of Arbitrary Boundary Conditions

(2009) K.S. McFall et al.   IEEE TRANSACTIONS ON NEURAL NETWORKS