Consistent dynamic mode decomposition

Omri Azencot, Wotao Yin, Andrea Bertozzi

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We propose a new method for computing dynamic mode decomposition evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of data alignment penalty terms and constitutive orthogonality constraints. Our method does not make any assumptions on the structure of the data or their size, and thus it is applicable to a wide range of problems including nonlinear scenarios or extremely small observation sets. In addition, our technique is robust to noise that is independent of the dynamics and it does not require input data to be sequential. Our key idea is to introduce a regularization term for the forward and backward dynamics. The obtained minimization problem is solved efficiently using the alternating method of multipliers (ADMM) which requires two Sylvester equation solves per iteration. Our numerical scheme converges empirically and is similar to a provably convergent ADMM scheme. We compare our approach to various state-of-The-Art methods on several benchmark dynamical systems.

Original languageEnglish
Pages (from-to)1565-1585
Number of pages21
JournalSIAM Journal on Applied Dynamical Systems
Volume18
Issue number3
DOIs
StatePublished - 1 Jan 2019
Externally publishedYes

Keywords

  • ADMM
  • Dynamic mode decomposition
  • Dynamical systems
  • Variational formulation

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