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.

中文翻译：

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通过信息瓶颈对混沌动力系统进行机器学习优化测量

确定性混沌允许“完美测量”的精确概念，当重复获得时，可以以最小的冗余捕获系统演化产生的所有信息。找到最佳测量方法具有挑战性，通常需要对少数情况下的动力学有深入的了解。我们在完美测量和信息瓶颈的变体之间建立了等价关系。因此，我们可以利用机器学习来优化测量过程，从而有效地从轨迹数据中提取信息。我们获得了多个混沌映射的近似最优测量，并为从一般时间序列中有效提取信息奠定了必要的基础。