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arXiv · 2312.08278

Invariant Consistent Dynamic Mode Decomposition

Gowtham S Seenivasaharagavan·Milan Korda·Hassan Arbabi·Igor Mezić
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Abstract

Any deterministic autonomous dynamical system may be globally linearized by its' Koopman operator. This object is typically infinite-dimensional and can be approximated by the so-called Dynamic Mode Decomposition (DMD). In DMD, the central idea is to preserve a fundamental property of the Koopman operator: linearity. This work augments DMD by preserving additional properties like functional relationships between observables and consistency along geometric invariants. The first set of constraints provides a framework for understanding DMD variants like Higher-order DMD and Affine DMD. The latter set guarantees the estimation of Koopman eigen-functions with eigen-value 1, whose level sets are known to delineate invariant sets. These benefits are realized with only a minimal increase in computational cost, primarily due to the linearity of constraints.

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Gowtham S Seenivasaharagavan, Milan Korda, Hassan Arbabi, Igor Mezić. 2023-12-13. Invariant Consistent Dynamic Mode Decomposition. https://arxiv.org/abs/2312.08278

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