# Learning Metastable Dynamics

arXiv: https://arxiv.org/abs/2609.14712 · HTML: https://mlsanity.com/paper/2609.14712/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 25 references that are in the map.
- First posted on arXiv 13 Sep 2026.

## Builds on (most cited first, 4 of 4)

- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Estimating Koopman operators with sketching to provably learn large scale dynamical systems](https://mlsanity.com/paper/2306.04520/) (2023)
- [Robust Moment Closure Method for the Chemical Master Equation](https://mlsanity.com/paper/1707.00178/) (2017)
- [Formal Analysis of Metastable Failures in Software Systems](https://mlsanity.com/paper/2510.03551/) (2025)

## Abstract (arXiv)

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.