Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition

2017/10/12 by Naoya Takeishi, Takeishi, Naoya, Yoshinobu Kawahara +3 · 22 citations
Engineering · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.1710.04340

openalex publication_date 2017/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often need to prepare nonlinear observables manually according to the underlying dynamics, which is not always possible since we may not have any a priori knowledge about them. In this paper, we propose a fully data-driven method for Koopman spectral analysis based on the principle of learning Koopman invariant subspaces from observed data. To this end, we propose minimization of the residual sum of squares of linear least-squares regression to estimate a set of functions that transforms data into a form in which the linear regression fits well. We introduce an implementation with neural networks and evaluate performance empirically using nonlinear dynamical systems and applications.

Citations

• Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification

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