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The well-known Mori-Zwanzig theory tells us that model reduction leads to memory effect.
General circulation experiments with the primitive equations: I. the basic experiment
Joseph Smagorinsky · 1963
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Transport, collective motion, and brownian motion
Hazime Mori · 1965
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Nonlinear generalized langevin equations
Robert Zwanzig · 1973
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Efficient implementation of essentially non-oscillatory shock-capturing schemes
Chi-Wang Shu and Stanley Osher · 1988
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Learning long-term dependencies with gradient descent is difficult
Yoshua Bengio, Patrice Simard, and Paolo Frasconi · 1994
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Long short-term memory
Sepp Hochreiter and Jürgen Schmidhuber · 1997
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Optimal prediction with memory
Alexandre J Chorin, Ole H Hald, and Raz Kupferman · 2002
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Variational boundary conditions for molecular dynamics simulations of crystalline solids at finite temperature: treatment of the thermal bath
Xiantao Li and Weinan E · 2007
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On the difficulty of training recurrent neural networks
Razvan Pascanu, Tomas Mikolov, and Yoshua Bengio · 2013
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Adam: A method for stochastic optimization
Diederik P Kingma and Jimmy Ba · 2014
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Reynolds averaged turbulence modelling using deep neural networks with embedded invariance
Julia Ling, Andrew Kurzawski, and Jeremy Templeton · 2016
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Quantifying and reducing model-form uncertainties in reynolds-averaged navier–stokes simulations: A data-driven, physics-informed bayesian approach
H Xiao, J-L Wu, J-X Wang, R Sun, and CJ Roy · 2016
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A thermodynamic study of the two-dimensional pressure-driven channel flow
Weinan E and Jianchun Wang · 2016
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Non-markovian closure models for large eddy simulations using the mori-zwanzig formalism
Eric J Parish and Karthik Duraisamy · 2017
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Computing the non-markovian coarse-grained interactions derived from the mori–zwanzig formalism in molecular systems: Application to polymer melts
Zhen Li, Hee Sun Lee, Eric Darve, and George Em Karniadakis · 2017
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Searching for turbulence models by artificial neural network
Masataka Gamahara and Yuji Hattori · 2017
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Subgrid-scale scalar flux modelling based on optimal estimation theory and machine-learning procedures
Antoine Vollant, Guillaume Balarac, and C Corre · 2017
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Data-based stochastic model reduction for the kuramoto–sivashinsky equation
Fei Lu, Kevin K. Lin, and Alexandre J. Chorin · 2016
Cited alongside, same era.
Physics-informed machine learning approach for reconstructing reynolds stress modeling discrepancies based on dns data
Jian-Xun Wang, Jin-Long Wu, and Heng Xiao · 2017
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