Attention Mechanisms in Dynamical Systems: A Case Study with Predator-Prey Models
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908357373198336 |
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| author | Balaban, David |
| author_facet | Balaban, David |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_06503 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Attention Mechanisms in Dynamical Systems: A Case Study with Predator-Prey Models Balaban, David Dynamical Systems Artificial Intelligence es: 92B05 (Primary), 34C60, 37N25, 68T07, 93B30 (Secondary) 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. |
| title | Attention Mechanisms in Dynamical Systems: A Case Study with Predator-Prey Models |
| topic | Dynamical Systems Artificial Intelligence es: 92B05 (Primary), 34C60, 37N25, 68T07, 93B30 (Secondary) |
| url | https://arxiv.org/abs/2505.06503 |