🤖 AI Summary
本文提出了一种从时间序列数据直接构建非循环物理过程预测模型的方法，无需假设微分方程。通过多尺度分析生成马尔可夫链形式的概率模型。
📝 Abstract
We introduce a method for constructing predictive models of non cyclic physical processes directly from time-series data, without assuming an underlying differential equation. The observations define a discrete evolution rule whose recurrent behaviour captures the essential dynamics of the process. Analysing this behaviour across multiple geometric scales leads to probabilistic models in the form of Markov chains. Hyperbolicity criteria identify when these models provide a consistent statistical description of the data. The method is inspired by, and illustrated through, the analysis of a biological imaging data set referred to as the Cell Process.