Maximally predictive states: From partial observations to long timescales

What is it about?

Complex structures in nature often arises from a limited set of simpler elements, such as novels from letters or proteins from amino acids. In musical composition, for example, we experience such construction in time; sounds and silences combine to form motifs; motifs form passages, which in turn form movements. But how can we generally identify nearly conserved long-lived structures from complex dynamics which are measured only incompletely? We introduce a novel framework for the identification of maximally-predictive states, from which we can identify long-lived structures through decomposing the ensemble dynamics into macroscopic structures that evolve on different timescales.

Featured Image

Photo by Daniele Levis Pelusi on Unsplash

Photo by Daniele Levis Pelusi on Unsplash

Why is it important?

Our framework allows us to distil the variables that accurately capture large scale phenomena, which is a fundamental step towards providing simplified interpretable models of complex dynamics.