Exploring complex pattern formation with convolutional neural networks

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 are 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 that we discuss in advanced undergraduate and graduate computational physics projects.