Koopman theory helps predict and analyze metastable states early
Learning Metastable Dynamics
PerformanceMachine Learning
Summary
Metastability happens when systems get stuck in nearly stable conditions before suddenly changing. This paper presents a new method that uses a mathematical tool called Koopman theory to find hidden patterns in system behavior. The authors show they can predict metastable behavior much earlier than before, even when only a small part of the data is available. They find that certain mathematical markers in their model can reliably indicate when metastability will occur.
What this means in practice
- •For industrial system engineers: Detect potential abrupt transitions in complex machinery or chemical processes significantly earlier to improve safety and maintenance planning.
- •For data center operators: Identify early signs of unstable states in server configurations to anticipate system failures or performance drops.
Authors
Rupak Majumdar, Mahmoud Salamati, Nikhil Singh, Sadegh Soudjani
Abstract
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.