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Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations, in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width.
Analysis of a complex of statistical variables into principal components
Harold Hotelling · 1933
Earlier work this paper cites.
Probability Theory
Michel Loeve · 1955
Earlier work this paper cites.
Beyond regression:” new tools for prediction and analysis in the behavioral sciences
Paul Werbos · 1974
Earlier work this paper cites.
Learnins logic
David B Parker · 1985
Earlier work this paper cites.
Learning representations by back-propagating errors
David E Rumelhart, Geoffrey E Hinton, and Ronald J Williams · 1986
Earlier work this paper cites.
Mathematics of control
George Cybenko · 1989
Earlier work this paper cites.
Nonlinear principal component analysis using autoassociative neural networks
Mark A Kramer · 1991
Earlier work this paper cites.
Reconstructing phase space from pde simulations
Michael Kirby and Dieter Armbruster · 1992
Earlier work this paper cites.
The proper orthogonal decomposition in the analysis of turbulent flows
Gal Berkooz, Philip Holmes, and John L Lumley · 1993
Earlier work this paper cites.
Neural-network-based approximations for solving partial differential equations
MWMG Dissanayake and N Phan-Thien · 1994
Earlier work this paper cites.
The numerical solution of linear ordinary differential equations by feedforward neural networks
Andrew J Meade Jr and Alvaro A Fernandez · 1994
Earlier work this paper cites.
Karhunen–loeve procedure for gappy data
Richard Everson and Lawrence Sirovich · 1995
Earlier work this paper cites.
Neural network differential equation and plasma equilibrium solver
B Ph van Milligen, V Tribaldos, and JA Jiménez · 1995
Earlier work this paper cites.
Artificial neural networks for solving ordinary and partial differential equations
Isaac E Lagaris, Aristidis Likas, and Dimitrios I Fotiadis · 1998
Earlier work this paper cites.
System Identification: Theory for the User
L. Ljung · 1999
Earlier work this paper cites.
Approximation theory of the mlp model in neural networks
Allan Pinkus · 1999
Earlier work this paper cites.
Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics
Karl Kunisch and Stefan Volkwein · 2002
Earlier work this paper cites.
Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: Error estimates and suboptimal control
Michael Hinze and Stefan Volkwein · 2005
Earlier work this paper cites.
Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems
Randall J LeVeque · 2007
Earlier work this paper cites.
The tradeoffs of large scale learning
Léon Bottou and Olivier Bousquet · 2008
Earlier work this paper cites.
Large-scale deep unsupervised learning using graphics processors
Rajat Raina, Anand Madhavan, and Andrew Y Ng · 2009
Earlier work this paper cites.
Nonlinear model reduction via discrete empirical interpolation
Saifon Chaturantabut and Danny C Sorensen · 2010
Earlier work this paper cites.
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Kevin Carlberg, Charbel Bou-Mosleh, and Charbel Farhat · 2011
Earlier work this paper cites.
Reduced order modeling based shape optimization of surface acoustic wave driven microfluidic biochips
Harbir Antil, Matthias Heinkenschloss, Ronald HW Hoppe, Christopher Linsenmann, and Achim Wixforth · 2012
Earlier work this paper cites.
Reduced order models for parameterized hyperbolic conservations laws with shock reconstruction
PG Constantine and G Iaccarino · 2012
Earlier work this paper cites.
The gnat method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
Kevin Carlberg, Charbel Farhat, Julien Cortial, and David Amsallem · 2013
Earlier work this paper cites.
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Gabriel Dimitriu, Ionel M Navon, and Răzvan Ştefănescu · 2013
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R Ştefănescu and Ionel Michael Navon · 2013
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Adam: A method for stochastic optimization, 2014
Diederik P. Kingma and Jimmy Ba · 2014
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Non-linear model reduction for the navier–stokes equations using residual deim method
Dunhui Xiao, Fangxin Fang, Andrew G Buchan, Christopher C Pain, Ionel Michael Navon, Juan Du, and G Hu · 2014
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Pod-deim based model order reduction for the spherical shallow water equations with turkel-zwas finite difference discretization
Pengfei Zhao, Cai Liu, and Xuan Feng · 2014
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The shifted proper orthogonal decomposition: A mode decomposition for multiple transport phenomena
Julius Reiss, Philipp Schulze, Jörn Sesterhenn, and Volker Mehrmann · 2018
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Transport reversal for model reduction of hyperbolic partial differential equations
Donsub Rim, Scott Moe, and Randall J LeVeque · 2018
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Dgm: A deep learning algorithm for solving partial differential equations
Justin Sirignano and Konstantinos Spiliopoulos · 2018
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The deep ritz method: a deep learning-based numerical algorithm for solving variational problems
E Weinan and Bing Yu · 2018
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Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations
Christian Beck, E Weinan, and Arnulf Jentzen · 2019
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