Information-driven transitions in projections of underdamped dynamics

TL;DR

This paper introduces an information-theoretic approach to modeling underdamped systems, revealing that optimal models can undergo abrupt transitions due to information loss minimization, with implications across various scientific fields.

Contribution

The authors develop a method using information projections to derive optimal low-dimensional models of underdamped dynamics, uncovering discontinuous transitions in model parameters.

Findings

Discontinuous transitions occur in optimal models due to information loss minimization.

The approach reveals fundamental properties of effective dynamical representations.

Results impact fields from biophysics to dimensionality reduction.

Abstract

Low-dimensional representations of underdamped systems often provide insightful grasps and analytical tractability. Here, we build such representations via information projections, obtaining an optimal model that captures the most information on observed spatial trajectories. We show that, in paradigmatic systems, the minimization of the information loss drives the appearance of a discontinuous transition in the optimal model parameters. Our results raise serious warnings for general inference approaches and unravel fundamental properties of effective dynamical representations, impacting several fields, from biophysics to dimensionality reduction.