Learning Collective Variables in Biological Systems

The first step when constructing a model of a system is to identify which details matter and which can be neglected. In many physical problems, the important, or relevant, features often correspond to slow collective variables and may be guessed based on knowledge about the system's underlying symmetries and conservation laws. Here, I show how to use machine learning to identify relevant variables in biological systems where they are otherwise hard to guess. In contexts from single cell mechanics to bacterial communities, I introduce deep learning methods that simplify the description of a system down to a handful of relevant features. Importantly, each approach is interpretable by construction. As a result, the discovered relevant variables, together with the equations they obey, reveal the hidden mechanisms underlying complex biological phenomena.