Attention Mechanisms in Dynamical Systems: A Case Study with Predator-Prey Models

TL;DR

This paper explores the use of attention mechanisms in modeling and analyzing classical dynamical systems, demonstrating their ability to reveal geometric and sensitivity properties in predator-prey models.

Contribution

It introduces a novel application of AI attention mechanisms for interpretability and sensitivity analysis in nonlinear dynamical systems, linking attention weights to system geometry.

Findings

Attention weights align with Lyapunov function geometry.

Attention-based weighting captures phase-space sensitivity.

Framework supports data-driven analysis without explicit equations.

Abstract

Attention mechanisms are widely used in artificial intelligence to enhance performance and interpretability. In this paper, we investigate their utility in modeling classical dynamical systems -- specifically, a noisy predator-prey (Lotka-Volterra) system. We train a simple linear attention model on perturbed time-series data to reconstruct system trajectories. Remarkably, the learned attention weights align with the geometric structure of the Lyapunov function: high attention corresponds to flat regions (where perturbations have small effect), and low attention aligns with steep regions (where perturbations have large effect). We further demonstrate that attention-based weighting can serve as a proxy for sensitivity analysis, capturing key phase-space properties without explicit knowledge of the system equations. These results suggest a novel use of AI-derived attention for interpretable, data-driven analysis and control of nonlinear systems. For example our framework could support future work in biological modeling of circadian rhythms, and interpretable machine learning for dynamical environments.