Exploring complex pattern formation with convolutional neural networks

TL;DR

This paper demonstrates how convolutional neural networks can efficiently classify, analyze, and discover complex spatiotemporal patterns in reaction-diffusion systems, exemplified by the Gray-Scott model, facilitating large-scale parameter space exploration.

Contribution

It introduces a machine learning approach using CNNs to automate pattern classification and discovery in reaction-diffusion systems, enhancing analysis efficiency and accessibility.

Findings

CNNs successfully classify diverse patterns in the Gray-Scott model.

The approach enables rapid exploration of parameter space.

Open source tools facilitate implementation in educational settings.

Abstract

Many nonequilibrium systems, such as biochemical reactions and socioeconomic interactions, can be described by reaction-diffusion equations that demonstrate a wide variety of complex spatiotemporal patterns. The diversity of the morphology of these patterns makes it difficult to classify them quantitatively and they are often described visually. Hence, searching through a large parameter space for patterns is a tedious manual task. We discuss how convolutional neural networks can be used to scan the parameter space, investigate existing patterns in more detail, and aid in finding new groups of patterns. As an example, we consider the Gray-Scott model for which training data is easy to obtain. Due to the popularity of machine learning in many scientific fields, well maintained open source toolkits are available that make it easy to implement the methods we discuss in advanced undergraduate and graduate computational physics projects.