Machine-learning optimized measurements of chaotic dynamical systems via the information bottleneck
This work addresses the challenge of efficiently extracting information from chaotic time series, which is incremental as it builds on existing information bottleneck methods for a specific domain.
The authors tackled the problem of finding optimal measurements for chaotic dynamical systems by establishing an equivalence between perfect measurements and a variant of the information bottleneck, enabling the use of machine learning to optimize measurement processes from trajectory data, with results applied to multiple chaotic maps.
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.