Attention Mechanisms in Dynamical Systems: A Case Study with Predator-Prey Models
This provides a novel, interpretable data-driven approach for analyzing nonlinear systems, with potential applications in biological modeling and machine learning, though it is incremental as it adapts existing attention methods to a new domain.
The paper tackled the problem of modeling noisy predator-prey dynamical systems by applying attention mechanisms to reconstruct trajectories, finding that learned attention weights align with Lyapunov function geometry and can serve as a proxy for sensitivity analysis.
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.