SelectNet: Self-paced learning for high-dimensional partial differential equations

Neural network approximation: Three hidden layers are enough

(2021) Zuowei Shen et al.   NEURAL NETWORKS

Weak adversarial networks for high-dimensional partial differential equations

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

Error bounds for deep ReLU networks using the Kolmogorov–Arnold superposition theorem

(2020) Hadrien Montanelli et al.   NEURAL NETWORKS

Computing committor functions for the study of rare events using deep learning

(2019) Qianxiao Li et al.   JOURNAL OF CHEMICAL PHYSICS

Nonlinear approximation via compositions

(2019) Zuowei Shen et al.   NEURAL NETWORKS

DGM: A deep learning algorithm for solving partial differential equations

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

Optimal approximation of piecewise smooth functions using deep ReLU neural networks

(2018) Philipp Petersen et al.   NEURAL NETWORKS

Approximation capability of two hidden layer feedforward neural networks with fixed weights

(2018) Namig J. Guliyev et al.   NEUROCOMPUTING

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

Exponential convergence of the deep neural network approximation for analytic functions

(2018) Weinan E et al.   Science China-Mathematics

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

Error bounds for approximations with deep ReLU networks

(2017) Dmitry Yarotsky   NEURAL NETWORKS