Estimates on the generalization error of physics-informed neural networks for approximating PDEs

Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs

(2021) Siddhartha Mishra et al.   IMA JOURNAL OF NUMERICAL ANALYSIS

A multi-level procedure for enhancing accuracy of machine learning algorithms

(2020) KJETIL O. LYE et al.   EUROPEAN JOURNAL OF APPLIED MATHEMATICS

Deep learning observables in computational fluid dynamics

(2020) Kjetil O. Lye et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Machine learning for fast and reliable solution of time-dependent differential equations

(2019) F. Regazzoni et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Physics-informed neural networks for high-speed flows

(2019) Zhiping Mao et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

An artificial neural network as a troubled-cell indicator

(2018) Deep Ray et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Hidden physics models: Machine learning of nonlinear partial differential equations

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

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

Error bounds for approximations with deep ReLU networks

(2017) Dmitry Yarotsky   NEURAL NETWORKS

Deep learning

(2015) Yann LeCun et al.   NATURE