Learning Metastable Dynamics

2026-09-13

AI Summary

为解决物理系统中识别和分析亚稳态现象的挑战，提出了一种基于Koopman理论的新框架，通过学习系统的动态表示来提前预测亚稳态行为。

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.

Problem

• Metastability
• Koopman theory
• latent space
• spectral properties
• eigenvalue

Innovation

• Koopman theory
• metastability analysis
• latent space
• spectral properties
• dominant eigenvalue