Machine-learning optimized measurements of chaotic dynamical systems via the information bottleneck

2023/11/08 by Kieran A. Murphy, Dani S. Bassett, Murphy, Kieran A. +1 · 1 citation
Computer Science · #Chaotic Dynamics (nlin.CD) #Computational Physics and Python Applications #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Machine Learning (cs.LG) #Neural Networks and Applications #Time Series Analysis and Forecasting

paper · pdf · doi:10.48550/arxiv.2311.04896

openalex publication_date 2023/11/08 · openalex created_date 2023/11/10 · openalex updated_date 2026/07/28

Abstract

Deterministic chaos permits a precise notion of a "perfect measurement" as one that, when obtained repeatedly, captures all of the information created by the system's evolution with minimal redundancy. Finding an optimal measurement is challenging, and has generally required intimate knowledge of the dynamics in the few cases where it has been done. We establish an equivalence between a perfect measurement and a variant of the information bottleneck. As a consequence, we can employ machine learning to optimize measurement processes that efficiently extract information from trajectory data. We obtain approximately optimal measurements for multiple chaotic maps and lay the necessary groundwork for efficient information extraction from general time series.

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