Model chaotic physical processes directly from time series data
Equation free data-driven modelling of chaotic processes
Information Theory
Summary
Predicting complex and irregular natural events, like certain biological processes, is difficult because they don't follow simple repeating patterns. This paper presents a way to build models directly from sequences of measurements, without needing to know the exact equations behind the process. The method uses patterns in the data's behavior across different scales to create statistical models that can describe how the system evolves. The authors show how their approach works using biological imaging data.
What this means in practice
- •For biomedical imaging teams: Build predictive models of biological processes from imaging data without needing predefined physical equations.
- •For environmental monitoring teams: Create statistical models for irregular natural phenomena using only observed time-series measurements, aiding in prediction and analysis.
Tested on one dataset.
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.