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

2026-04-27

AI Summary

This work addresses the challenge of unsupervised identification of latent state variables in dynamical systems from high-dimensional observations by introducing Dynamic Symmetric Information Bottleneck (DySIB). The method learns low-dimensional dynamical representations by maximizing the predictive mutual information between past and future observation windows within a fully latent space, while simultaneously penalizing representational complexity—without requiring reconstruction of the original data. DySIB is the first approach to self-consistently recover a phase space with the correct dimensionality, topology, and geometric structure, yielding interpretable coordinates. In experiments on real video data of a physical pendulum, DySIB successfully reconstructs a two-dimensional phase space whose structure aligns with that of the true system, with latent variables smoothly corresponding to the physical angle and angular velocity.

Technology Category

• Machine Learning: Learning with Manifolds
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

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.

Problem

• dynamical state variables
• high-dimensional data
• phase space
• unsupervised learning
• time-series

Innovation

• Information Bottleneck
• Dynamical Systems
• Latent Representation
• Predictive Mutual Information
• Unsupervised Learning