Information bottleneck for learning the phase space of dynamics from high-dimensional experimental data

TL;DR

This paper introduces DySIB, a method for learning low-dimensional, interpretable dynamical representations from high-dimensional time-series data by maximizing predictive mutual information in latent space.

Contribution

DySIB is a novel approach that infers dynamical state variables directly from raw data without reconstruction, matching known phase space properties in experiments.

Findings

DySIB recovers a 2D phase space matching the pendulum's topology.

The learned coordinates align with canonical angle and angular velocity.

The method operates entirely in latent space, avoiding data reconstruction.

Abstract

Identifying the dynamical state variables of a system from high-dimensional observations is a central problem across physical sciences. The challenge is that the state variables are not directly observable and must be inferred from raw high-dimensional data without supervision. Here we introduce DySIB (Dynamical Symmetric Information Bottleneck) as a method to learn low-dimensional representations of time-series data by maximizing predictive mutual information between past and future observation windows while penalizing representation complexity. This objective operates entirely in latent space and avoids reconstruction of the observations. We apply DySIB to an experimental video dataset of a physical pendulum, where the underlying state space is known. The method, with hyperparameters of the learning architecture set self-consistently by the data, recovers a two-dimensional representation that matches the dimensionality, topology, and geometry of the pendulum phase space, with the learned coordinates aligning smoothly with the canonical angle and angular velocity. These results demonstrate, on a well-characterized experimental system, that predictive information in latent space can be used to recover interpretable dynamical coordinates directly from high-dimensional data.