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Gowtham S Seenivasaharagavan

Publications and source records attributed to Gowtham S Seenivasaharagavan.

2 recordsLinked to original sources
arXiv2025

Clarifying the effect of mean subtraction on Dynamic Mode Decomposition

Any autonomous nonlinear dynamical system can be viewed as a superposition of infinitely many linear processes, through the so-called Koopman mode decomposition. Its data-driven approximation- Dynamic Mode Decomposition (DMD)- has been extensively developed and deployed across a plethora of fields. In this work, we study the effect of subtracting the temporal mean on the DMD approximation, for observables possessing only a finite number of Koopman modes. Pre-processing time-sequential training data by removing the temporal mean has been a point of contention in the Companion matrix formulation of DMD. This stems from the potential of said pre-processing to render DMD equivalent to a temporal Discrete Fourier Transform (DFT). We prove that this equivalence is impossible when the training data is linearly consistent and the order of the DMD model exceeds the number of Koopman modes. Since model order and training set size are synonymous in this variant of DMD, the parity of DMD and DFT can, therefore, be indicative of inadequate training data.

math.DS↗
arXiv2023

Invariant Consistent Dynamic Mode Decomposition

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.

math.DS↗