Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Generalizing dynamic mode decomposition: balancing accuracy
and expressiveness in Koopman approximations
M. Haseli, J. Cortés
Automatica 153 (2023), 111001
Abstract
This paper tackles the data-driven approximation of unknown
dynamical systems using Koopman-operator methods. Given a
dictionary of functions, these methods approximate the projection of
the action of the operator on the finite-dimensional subspace
spanned by the dictionary. We propose the Tunable Symmetric
Subspace Decomposition algorithm to refine the dictionary, balancing
its expressiveness and accuracy. Expressiveness corresponds to the
ability of the dictionary to describe the evolution of as many
observables as possible and accuracy corresponds to the ability to
correctly predict their evolution. Based on the observation that
Koopman-invariant subspaces give rise to exact predictions, we
reason that prediction accuracy is a function of the degree of
invariance of the subspace generated by the dictionary and provide a
data-driven measure to measure invariance proximity. The proposed
algorithm iteratively prunes the initial functional space to
identify a refined dictionary of functions that satisfies the
desired level of accuracy while retaining as much of the original
expressiveness as possible. We provide a full characterization of the
algorithm properties and show that it generalizes both Extended
Dynamic Mode Decomposition and Symmetric Subspace
Decomposition. Simulations on planar systems show the effectiveness
of the proposed methods in producing Koopman approximations of
tunable accuracy that capture relevant information about the
dynamical system.
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Mechanical and Aerospace Engineering,
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