Characterizing information loss in a chaotic double pendulum with the Information Bottleneck

TL;DR

This paper uses the Information Bottleneck method with neural networks to analyze how information about a chaotic double pendulum's state degrades over time, revealing variable importance in future predictions.

Contribution

It introduces a novel machine learning framework to decompose and quantify information loss in chaotic systems using the Information Bottleneck approach.

Findings

Identifies the relative importance of system variables in predicting future states.

Provides a practical method to monitor predictability limits in chaotic dynamics.

Demonstrates broad applicability to different chaotic systems.

Abstract

A hallmark of chaotic dynamics is the loss of information with time. Although information loss is often expressed through a connection to Lyapunov exponents -- valid in the limit of high information about the system state -- this picture misses the rich spectrum of information decay across different levels of granularity. Here we show how machine learning presents new opportunities for the study of information loss in chaotic dynamics, with a double pendulum serving as a model system. We use the Information Bottleneck as a training objective for a neural network to extract information from the state of the system that is optimally predictive of the future state after a prescribed time horizon. We then decompose the optimally predictive information by distributing a bottleneck to each state variable, recovering the relative importance of the variables in determining future evolution. The framework we develop is broadly applicable to chaotic systems and pragmatic to apply, leveraging data and machine learning to monitor the limits of predictability and map out the loss of information.