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

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

(2020) Maziar Raissi et al.   SCIENCE

Deep learning observables in computational fluid dynamics

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

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

Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization

(2018) Benjamin Peherstorfer et al.   SIAM REVIEW

Error bounds for approximations with deep ReLU networks

(2017) Dmitry Yarotsky   NEURAL NETWORKS

Entropy Stable Scheme on Two-Dimensional Unstructured Grids for Euler Equations

(2016) Deep Ray et al.   Communications in Computational Physics

Deep learning

(2015) Yann LeCun et al.   NATURE

Multilevel Monte Carlo methods

(2015) Michael B. Giles   ACTA NUMERICA

Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions

(2012) S. Mishra et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data

(2012) S. Mishra et al.   MATHEMATICS OF COMPUTATION

Multilevel Monte Carlo Path Simulation

(2008) Michael B. Giles   OPERATIONS RESEARCH