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.
|ジャーナル||Advances in Neural Information Processing Systems|
|出版ステータス||出版済み - 2017|
|イベント||31st Annual Conference on Neural Information Processing Systems, NIPS 2017 - Long Beach, 米国|
継続期間: 12 4 2017 → 12 9 2017
All Science Journal Classification (ASJC) codes
- コンピュータ ネットワークおよび通信