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Title: 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 data-driven 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. cyber-physical infrastructure systems, biological networks, social systems, and fluid dynamics. Often the dictionaries generated for these problems are manually curated, requiring domain-specific 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 state-of-the-art 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:
 [1]; ORCiD logo [1]; ORCiD logo [1]
  1. 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):
PNNL-SA-128573
DOE Contract Number:  
AC05-76RL01830
Resource Type:
Conference
Resource Relation:
Conference: Proceedings of the American Control Conference, July 10-12, 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 data-driven 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. cyber-physical infrastructure systems, biological networks, social systems, and fluid dynamics. Often the dictionaries generated for these problems are manually curated, requiring domain-specific 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 state-of-the-art 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}
}

Conference:
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