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Physics > Computational Physics

arXiv:2412.03734 (physics)
[Submitted on 4 Dec 2024]

Title:A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations

Authors:Andre N. Souza, Simone Silvestri
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Abstract:We investigate the convergence behavior of the extended dynamic mode decomposition for constructing a discretization of the continuity equation associated with the Lorenz equations using a nonlinear dictionary of over 1,000,000 terms. The primary objective is to analyze the resulting operator by varying the number of terms in the dictionary and the timescale. We examine what happens when the number of terms of the nonlinear dictionary is varied with respect to its ability to represent the invariant measure, Koopman eigenfunctions, and temporal autocorrelations. The dictionary comprises piecewise constant functions through a modified bisecting k-means algorithm and can efficiently scale to higher-dimensional systems.
Subjects: Computational Physics (physics.comp-ph)
Cite as: arXiv:2412.03734 [physics.comp-ph]
  (or arXiv:2412.03734v1 [physics.comp-ph] for this version)
  https://doi.org/10.48550/arXiv.2412.03734

Submission history

From: Andre Souza [view email]
[v1] Wed, 4 Dec 2024 21:58:10 UTC (23,946 KB)
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