Characterizing information loss in a chaotic double pendulum with the Information Bottleneck
This work provides a new framework for studying information decay in chaotic dynamics, which is incremental but offers practical tools for predictability analysis in such systems.
The authors tackled the problem of characterizing information loss in chaotic systems, specifically using a double pendulum, by applying the Information Bottleneck with neural networks to extract predictive information about future states, revealing the relative importance of state variables.
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.