Data driven models predict complex physical processes without equations
Equation free data-driven modelling of chaotic processes
Information Theory
Summary
Predicting how complicated systems change over time is often difficult because their rules aren’t clear or simple. This paper shows a way to build models directly from sequences of observations, without guessing any underlying formulas. The authors use recurring patterns found in the data to create a kind of probabilistic map that captures the system’s behavior on different scales. They test this approach using biological cell imaging data, showing it can describe how the cells evolve statistically.
time seriespredictive modelchaotic processdiscrete evolutionMarkov chainprobabilistic modelhyperbolicitystatistical descriptionbiological imagingdynamical systems
Authors
Aurora Poggi, Marco Martens, Hjalmar Brismar, Ozan Oktem, Liviana Palmisano
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.