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High-dimensional spatio-temporal dynamics can often be encoded in a low-dimensional subspace.
Probability theory: foundations, random sequences
Michel Loeve · 1955
Earlier work this paper cites.
The structure of inhomogeneous turbulent flows
John Leask Lumley · 1967
Earlier work this paper cites.
Adaptive mesh refinement for hyperbolic partial differential equations
Marsha J Berger and Joseph Oliger · 1984
Earlier work this paper cites.
Insight into the dynamics of coherent structures from a proper orthogonal decomposition dy
William K George · 1988
Earlier work this paper cites.
Multilayer feedforward networks are universal approximators
Kurt Hornik, Maxwell Stinchcombe, Halbert White, et al · 1989
Earlier work this paper cites.
The route to chaos for the kuramoto-sivashinsky equation
Demetrios T Papageorgiou and Yiorgos S Smyrlis · 1991
Earlier work this paper cites.
Learning to control fast-weight memories: An alternative to dynamic recurrent networks
Jürgen Schmidhuber · 1992
Earlier work this paper cites.
Multidisciplinary aerospace design optimization: survey of recent developments
Jaroslaw Sobieszczanski-Sobieski and Raphael T Haftka · 1997
Earlier work this paper cites.
An improved in situ and satellite sst analysis for climate
Richard W Reynolds, Nick A Rayner, Thomas M Smith, Diane C Stokes, and Wanqiu Wang · 2002
Earlier work this paper cites.
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Romain Teyssier · 2002
Earlier work this paper cites.
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Earlier work this paper cites.
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Bernd R Noack, Konstantin Afanasiev, MAREK MORZYŃSKI, Gilead Tadmor, and Frank Thiele · 2003
Earlier work this paper cites.
Model reduction for compressible flows using pod and galerkin projection
Clarence W Rowley, Tim Colonius, and Richard M Murray · 2004
Earlier work this paper cites.
Application of adaptive mesh refinement to particle-in-cell simulations of plasmas and beams
J-L Vay, P Colella, JW Kwan, P McCorquodale, DB Serafini, A Friedman, DP Grote, G Westenskow, J-C Adam, A Heron, et al · 2004
Earlier work this paper cites.
Paraview: An end-user tool for large data visualization
James Ahrens, Berk Geveci, and Charles Law · 2005
Earlier work this paper cites.
Fourth-order time-stepping for stiff pdes
Aly-Khan Kassam and Lloyd N Trefethen · 2005
Earlier work this paper cites.
A parallelized, adaptive algorithm for multiphase flows in general geometries
Mark Sussman · 2005
Earlier work this paper cites.
The immersed boundary method: a projection approach
Kunihiko Taira and Tim Colonius · 2007
Earlier work this paper cites.
On the optimality of the proper orthogonal decomposition and balanced truncation
Seddik M Djouadi · 2008
Earlier work this paper cites.
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Earlier work this paper cites.
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William M Chan · 2009
Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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M. Frangos, Y. Marzouk, K. Willcox, and B. van Bloemen Waanders · 2010
Earlier work this paper cites.
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Earlier work this paper cites.
A critical-layer framework for turbulent pipe flow
Beverley J McKeon and Ati S Sharma · 2010
Earlier work this paper cites.
Dynamic mode decomposition of numerical and experimental data
Peter J Schmid · 2010
Earlier work this paper cites.
Computer vision: algorithms and applications
Richard Szeliski · 2010
Earlier work this paper cites.
Adaptive methods for simulation of turbulent combustion
John Bell and Marcus Day · 2011
Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Thomas JR Hughes · 2012
Earlier work this paper cites.
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Earlier work this paper cites.
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A Nonaka, JB Bell, MS Day, C Gilet, AS Almgren, and ML Minion · 2012
Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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James L Flanagan · 2013
Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Greg L Bryan, Michael L Norman, Brian W O’Shea, Tom Abel, John H Wise, Matthew J Turk, Daniel R Reynolds, David C Collins, Peng Wang, Samuel W Skillman, et al · 2014
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Stefan Van der Walt, Johannes L Schönberger, Juan Nunez-Iglesias, François Boulogne, Joshua D Warner, Neil Yager, Emmanuelle Gouillart, and Tony Yu · 2014
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