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.

翻译：确定性混沌允许对“完美测量”有一个精确的定义——即当重复获取时，它能以最小冗余捕获系统演化产生的全部信息。寻找最优测量极具挑战性，在少数成功案例中通常需要对动力学有深入理解。我们建立了完美测量与信息瓶颈变体之间的等价关系。因此，我们可以利用机器学习来优化测量过程，从而高效地从轨迹数据中提取信息。我们为多个混沌映射获得了近似最优的测量，并为从一般时间序列中高效提取信息奠定了必要基础。