A machine learning framework for data driven acceleration of computations of differential equations

Multilayer feedforward networks are universal approximators

K. Hornik, M. Stinchcombe, and H. White · 1989

Earlier work this paper cites.

Hyperbolic Systems of Conservation Laws

Edwige Godlewski and Pierre A. Raviart · 1991

Earlier work this paper cites.

Solving ordinary differential equations ,

E. Hairer and G. Wanner · 1991

Earlier work this paper cites.

Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans. Inform. Theory, 39(3), 930-945, 1993

A. R. Barron · 1993

Earlier work this paper cites.

Spectral methods in MATLAB ,

L. N. Trefethen · 2000

Earlier work this paper cites.

Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems

E. Tadmor · 2003

Earlier work this paper cites.

Hyperbolic Conservation Laws in Continuum Physics (2nd Ed.)

Constantine M. Dafermos · 2005

Earlier work this paper cites.

Finite difference methods for ordinary and partial differential equations, steady state and time dependent problems

R. J. LeVeque · 2007

Earlier work this paper cites.

The mathematical theory of finite element methods

S. C. Brenner and L. R. Scott · 2008

Earlier work this paper cites.

Inverse problems: a Bayesian perspective

A. M. Stuart · 2010

Earlier work this paper cites.

Optimal control of partial differential equations

F. Troltzsch · 2010

Cited alongside, same era.

Sum-product Networks: A new deep architecture

H. Poon and P. Domingos · 2011

Cited alongside, same era.

Computational optimization of systems governed by partial differential equations

A. Borzi and V. Schulz · 2012

Cited alongside, same era.

Arbitrarily high-order order accurate essentially non-oscillatory entropy stable schemes for systems of conservation laws

U. S. Fjordholm, S. Mishra and E. Tadmor · 2012

Cited alongside, same era.

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

S. Mishra, Ch. Schwab and J. Šukys · 2012

Cited alongside, same era.

Uncertainty quantification in computational fluid dynamics.,

H. Bijl, D. Lucor, S. Mishra and Ch. Schwab. (editors) · 2014

Deep learning ,

I. Goodfellow. Y. Bengio and A. Courville · 2016

Later among the works it cites.

Machine learning approximation algorithms for high dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations

C. Beck, W. E, and A. Jentzen · 2017

Later among the works it cites.

An efficient deep learning technique for the Navier-Stokes equations: application to unsteady wake flow dynamics

T. P. Miyanawala and R. K, Jaiman · 2017

Later among the works it cites.

An overview of gradient descent optimization algorithms

S. Ruder · 2017

Later among the works it cites.

Deep learning in high dimension

C. Schwab and J. Zech · 2017

Later among the works it cites.

Accelarating Eulerian fluid simulation with convolutional networks