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Characterizing Complex Spatiotemporal Patterns from Entropy Measures

journal contribution
posted on 2024-06-13, 16:32 authored by Luan Orion Barauna, Rubens Andreas Sautter, Reinaldo Roberto Rosa, Erico Luiz Rempel, Alejandro FreryAlejandro Frery
In addition to their importance in statistical thermodynamics, probabilistic entropy measurements are crucial for understanding and analyzing complex systems, with diverse applications in time series and one-dimensional profiles. However, extending these methods to two- and three-dimensional data still requires further development. In this study, we present a new method for classifying spatiotemporal processes based on entropy measurements. To test and validate the method, we selected five classes of similar processes related to the evolution of random patterns: (i) white noise; (ii) red noise; (iii) weak turbulence from reaction to diffusion; (iv) hydrodynamic fully developed turbulence; and (v) plasma turbulence from MHD. Considering seven possible ways to measure entropy from a matrix, we present the method as a parameter space composed of the two best separating measures of the five selected classes. The results highlight better combined performance of Shannon permutation entropy (SHp) and a new approach based on Tsallis Spectral Permutation Entropy (Sqs). Notably, our observations reveal the segregation of reaction terms in this SHp×Sqs space, a result that identifies specific sectors for each class of dynamic process, and it can be used to train machine learning models for the automatic classification of complex spatiotemporal patterns.

History

Preferred citation

Barauna, L. O., Sautter, R. A., Rosa, R. R., Rempel, E. L. & Frery, A. C. (n.d.). Characterizing Complex Spatiotemporal Patterns from Entropy Measures. Entropy, 26(6), 508-508. https://doi.org/10.3390/e26060508

Journal title

Entropy

Volume

26

Issue

6

Pagination

508-508

Publisher

MDPI AG

Publication status

Published online

Online publication date

2024-06-12

eISSN

1099-4300

Language

en

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