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In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs.
Über die partiellen Differenzengleichungen der mathematischen Physik
R. Courant, K. Friedrichs, and H. Lewy · 1928
Earlier work this paper cites.
Hamiltonian systems and transformation in hilbert space
B. O. Koopman · 1931
Earlier work this paper cites.
Uber die beste annaherung von funktionen einer gegebenen funktionenklasse
A. Kolmogoroff · 1936
Earlier work this paper cites.
Discrete Variable Methods in Ordinary Differential Equations
P. Henrici · 1962
Earlier work this paper cites.
Runge-kutta methods with minimum error bounds
Anthony Ralston · 1962
Earlier work this paper cites.
Ordinary Differential Equations
V.I. Arnold and R.A. Silverman · 1978
Earlier work this paper cites.
Autoencoders, minimum description length and helmholtz free energy
Geoffrey E Hinton and Richard Zemel · 1993
Earlier work this paper cites.
Long short-term memory
Sepp Hochreiter and Jürgen Schmidhuber · 1997
Earlier work this paper cites.
Learning to forget: Continual prediction with lstm
Felix A. Gers, Jürgen Schmidhuber, and Fred Cummins · 2000
Earlier work this paper cites.
Sobolev Spaces
R.A. Adams and J.J.F. Fournier · 2003
Earlier work this paper cites.
An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations
Maxime Barrault, Yvon Maday, Ngoc Cuong Nguyen, and Anthony T. Patera · 2004
Earlier work this paper cites.
A priori hyperreduction method: an adaptive approach
D. Ryckelynck · 2005
Earlier work this paper cites.
Galerkin finite element methods for parabolic problems
Vidar Thomee · 2006
Earlier work this paper cites.
Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
Martin A. Grepl, Yvon Maday, Ngoc C. Nguyen, and Anthony T. Patera · 2007
Earlier work this paper cites.
Numerical Mathematics
Alfio Quarteroni, Riccardo Sacco, and Fausto Saleri · 2007
Earlier work this paper cites.
Numerical approximation of partial differential equations
Alfio Quarteroni and Alberto Valli · 2008
Earlier work this paper cites.
Nonlinear model reduction via discrete empirical interpolation
Saifon Chaturantabut and Danny C. Sorensen · 2010
Earlier work this paper cites.
Dynamic mode decomposition of numerical and experimental data
Peter J Schmid · 2010
Earlier work this paper cites.
A survey of projection-based model reduction methods for parametric dynamical systems
Peter Benner, Serkan Gugercin, and Karen Willcox · 2015
Earlier work this paper cites.
Batch normalization: Accelerating deep network training by reducing internal covariate shift, 2015
Sergey Ioffe and Christian Szegedy · 2015
Earlier work this paper cites.
Efficient model reduction of parametrized systems by matrix discrete empirical interpolation
Federico Negri, Andrea Manzoni, and David Amsallem · 2015
Earlier work this paper cites.
Reduced Basis Methods for Partial Differential Equations: An Introduction
A. Quarteroni, A. Manzoni, and F. Negri · 2015
Earlier work this paper cites.
Embed to control: A locally linear latent dynamics model for control from raw images
Manuel Watter, Jost Springenberg, Joschka Boedecker, and Martin Riedmiller · 2015
Earlier work this paper cites.
Layer normalization, 2016
Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E. Hinton · 2016
Earlier work this paper cites.
Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control
Steven L Brunton, Bingni W Brunton, Joshua L Proctor, and J Nathan Kutz · 2016
Earlier work this paper cites.
Discovering governing equations from data by sparse identification of nonlinear dynamical systems
Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz · 2016
Earlier work this paper cites.
Fast and accurate deep network learning by exponential linear units (elus), 2016
Djork-Arné Clevert, Thomas Unterthiner, and Sepp Hochreiter · 2016
Earlier work this paper cites.
Hypernetworks, 2016
David Ha, Andrew Dai, and Quoc V. Le · 2016
Earlier work this paper cites.
Identity mappings in deep residual networks
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2016
Earlier work this paper cites.
A proposal on machine learning via dynamical systems
Weinan E · 2017
Earlier work this paper cites.
DR-RNN: A deep residual recurrent neural network for model reduction, 2017
J. Nagoor Kani and Ahmed H. Elsheikh · 2017
Earlier work this paper cites.
Adam: A method for stochastic optimization, 2017
Diederik P. Kingma and Jimmy Ba · 2017
Earlier work this paper cites.
Film: Visual reasoning with a general conditioning layer, 2017
Ethan Perez, Florian Strub, Harm de Vries, Vincent Dumoulin, and Aaron Courville · 2017
Earlier work this paper cites.
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Ricky T. Q. Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud · 2018
Earlier work this paper cites.
Francisco J Gonzalez and Maciej Balajewicz · 2018
Earlier work this paper cites.
Non-intrusive reduced order modeling of nonlinear problems using neural networks
Jan S. Hesthaven and Stefano Ubbiali · 2018
Earlier work this paper cites.
Beyond finite layer neural networks: Bridging deep architectures and numerical differential equations
Yiping Lu, Aoxiao Zhong, Quanzheng Li, and Bin Dong · 2018
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Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks
Pantelis R. Vlachas, Wonmin Byeon, Zhong Y. Wan, Themistoklis P. Sapsis, and Petros Koumoutsakos · 2018
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Model identification of reduced order fluid dynamics systems using deep learning
Z. Wang, D. Xiao, F. Fang, R. Govindan, C. C. Pain, and Y. Guo · 2018
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