Characterizing nonlinear dynamics by contrastive cartography

TL;DR

This paper introduces a contrastive learning-based, model-free method for characterizing complex nonlinear dynamical systems from trajectory data, enabling automatic discovery of dynamical classes and phase diagrams without prior knowledge.

Contribution

It presents a novel contrastive cartography approach that automatically identifies dynamical behaviors and phase diagrams from stochastic data, applicable across various systems.

Findings

Successfully recovers known dynamical phase diagrams

Provides a map of behaviors for diverse systems

Characterizes bacterial motion without prior models

Abstract

The qualitative study of dynamical systems using bifurcation theory is key to understanding systems from biological clocks and neurons to physical phase transitions. Data generated from such systems can feature complex transients, an unknown number of attractors, and stochasticity. Characterization of these often-complicated behaviors remains challenging. Making an analogy to bifurcation analysis, which specifies that useful dynamical features are often invariant to coordinate transforms, we leverage contrastive learning to devise a generic tool to discover dynamical classes from stochastic trajectory data. By providing a model-free trajectory analysis tool, this method automatically recovers the dynamical phase diagram of known models and provides a "map" of dynamical behaviors for a large ensemble of dynamical systems. The method thus provides a way to characterize and compare dynamical trajectories without governing equations or prior knowledge of target behavior. We additionally show that the same strategy can be used to characterize the stochastic motion of bacteria, establishing that this approach can be used as a standalone analysis tool or as a component of a broader data-driven analysis framework for dynamical data.