Metastability---a phenomenon where systems remain trapped in quasi-stable states before abruptly transitioning under rare perturbations---is ubiquitous in physical systems. Although metastability is a widely observed phenomenon, its identification and analysis present significant challenges. To address these challenges, we propose a novel framework for analyzing metastability using Koopman theory. We use a finite set of system trajectories to learn a representation of the dynamics that defines a latent space in which the system evolves linearly, thereby enabling a systematic characterization of metastable behavior through the spectral properties of the linear mapping. Empirical evaluations demonstrate that our approach is capable of anticipating metastable behavior significantly earlier than its actual manifestation, even with 10% of the simulation duration. Moreover, we establish that the dominant eigenvalue of the learned Koopman matrix in the latent space serves as a critical indicator for detecting metastability across both single-server and multi-server configurations.
Figures & tables
Figure 1. Average latency (top) and Average queue length (bottom) for different arrival rates.
Figure 2. Illustrating the learned model performance for trajectories initialized from empty queue (top plot) and full queue (bottom plot).
Figure 3. The largest eigenvalue of the Koopman matrix for different values of arrival rates.
Figure 4. Illustrating the effect of throttling on the average queue length.
Figure 5. Comparison of average latency under LIFO and FIFO scheduling policies.
Figure 6. Comparison of average queue length under LIFO and FIFO scheduling policies.
Figure 7. Illustrating the performance of the learned model when trained on shorter-duration trajectories.
Figure 8. Variation in settling time in the original space as a function of δ (top plot) and in the latent space as a function of δ^ (bottom plot).
Figure 9. Average latency in the two-server system.
Figure 10. Average queue length in the two-server system.
Figure 11. Variation in settling time as a function of δ^ .
Dynamical systems studies how states evolve over time, including stability, feedback, chaos, and transitions in physical, biological, and engineered systems.
RIKEN Center for Advanced Intelligence Project, Tokyo, Japan. · Graduate School of Information Science and Technology, The University of Osaka, Suita, Osaka, Japan.