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

arXiv:2311.04896v2 Announce Type: replace
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 …

abstract arxiv chaos cs.it cs.lg dynamics evolution information knowledge machine math.it measurement nlin.cd notion redundancy systems the information type via