Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems
2019 American Control Conference (ACC)(2017)
摘要
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.
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关键词
deep neural network representations,Koopman operator,nonlinear dynamical systems,dynamical systems analysis,data-driven model discovery,extended dynamic mode decomposition,cyber-physical infrastructure systems,biological networks,social systems,fluid dynamics,domain-specific knowledge,painstaking tuning,deep learning,partially observed nonlinear systems,Koopman operator learning,deep dictionaries,computational complexity,glycolytic oscillator
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