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.
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.
Read the Original
This page is a summary of: Maximally predictive states: From partial observations to long timescales, Chaos An Interdisciplinary Journal of Nonlinear Science, February 2023, American Institute of Physics, DOI: 10.1063/5.0129398.
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This repository contains the main scripts for the maximally predictive state space reconstruction and ensemble dynamics. The data for reproducing the figures can be found in https://zenodo.org/record/7130012#.ZBhlzOzML6s Any comments or questions, contact antoniocbscosta(at)gmail(dot)com. Also, suggestions to speed up the code are more than welcome!
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