Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems
Abstract
The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and datadriven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode decomposition; this requires a combinatorially large basis set to adequately describe many nonlinear systems of interest, e.g. cyberphysical infrastructure systems, biological networks, social systems, and fluid dynamics. Often the dictionaries generated for these problems are manually curated, requiring domainspecific knowledge and painstaking tuning. In this paper we introduce a deep learning framework for learning Koopman operators of nonlinear dynamical systems. We show that this novel method automatically selects efficient deep dictionaries, outperforming stateoftheart methods. We benchmark this method on partially observed nonlinear systems, including the glycolytic oscillator and show it is able to predict quantitatively 100 steps into the future, using only a single timepoint, and qualitative oscillatory behavior 400 steps into the future.
 Authors:

 BATTELLE (PACIFIC NW LAB)
 Publication Date:
 Research Org.:
 Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1568808
 Report Number(s):
 PNNLSA128573
 DOE Contract Number:
 AC0576RL01830
 Resource Type:
 Conference
 Resource Relation:
 Conference: Proceedings of the American Control Conference, July 1012, 2019, Philadelphia, PA
 Country of Publication:
 United States
 Language:
 English
 Subject:
 koopman operators, machine learning, deep learning, dynamic mode decomposition
Citation Formats
Yeung, Enoch H., Kundu, Soumya, and Hodas, Nathan O. Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems. United States: N. p., 2019.
Web.
Yeung, Enoch H., Kundu, Soumya, & Hodas, Nathan O. Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems. United States.
Yeung, Enoch H., Kundu, Soumya, and Hodas, Nathan O. Thu .
"Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems". United States.
@article{osti_1568808,
title = {Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems},
author = {Yeung, Enoch H. and Kundu, Soumya and Hodas, Nathan O.},
abstractNote = {The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and datadriven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode decomposition; this requires a combinatorially large basis set to adequately describe many nonlinear systems of interest, e.g. cyberphysical infrastructure systems, biological networks, social systems, and fluid dynamics. Often the dictionaries generated for these problems are manually curated, requiring domainspecific knowledge and painstaking tuning. In this paper we introduce a deep learning framework for learning Koopman operators of nonlinear dynamical systems. We show that this novel method automatically selects efficient deep dictionaries, outperforming stateoftheart methods. We benchmark this method on partially observed nonlinear systems, including the glycolytic oscillator and show it is able to predict quantitatively 100 steps into the future, using only a single timepoint, and qualitative oscillatory behavior 400 steps into the future.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {8}
}