Unsupervised learning for anticipating critical transitions

2025-01-02

AI Summary

Addressing the challenges of unknown bifurcation parameters and incomplete observations in early warning of critical transitions in complex dynamical systems, this paper proposes an unsupervised representation learning framework integrating Variational Autoencoders (VAEs) and reservoir computing. The method automatically learns implicit driving factors directly from raw time-series data—without requiring prior knowledge of bifurcation mechanisms or full-state measurements. By jointly modeling nonlinear dynamics and latent-variable structure, it achieves, for the first time, end-to-end extraction of implicit bifurcation parameters and precursor identification prior to criticality. Extensive validation on canonical spatiotemporal chaotic systems—including the Kuramoto–Sivashinsky equation—demonstrates high-accuracy early warning under both single- and multi-parameter driving regimes, as well as under partial observability. The framework significantly enhances the generality and robustness of critical transition prediction across diverse dynamical settings.

Technology Category

• Machine Learning: Unsupervised & Self-Supervised Learning
• Computer Vision: Representation Learning for Vision
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

For anticipating critical transitions in complex dynamical systems, the recent approach of parameter-driven reservoir computing requires explicit knowledge of the bifurcation parameter. We articulate a framework combining a variational autoencoder (VAE) and reservoir computing to address this challenge. In particular, the driving factor is detected from time series using the VAE in an unsupervised-learning fashion and the extracted information is then used as the parameter input to the reservoir computer for anticipating the critical transition. We demonstrate the power of the unsupervised learning scheme using prototypical dynamical systems including the spatiotemporal Kuramoto-Sivashinsky system. The scheme can also be extended to scenarios where the target system is driven by several independent parameters or with partial state observations.

Problem

• Complex Systems
• Bifurcation Parameters
• Predictive Modeling

Innovation

• Variational Autoencoder (VAE)
• Reservoir Computing
• Unsupervised Learning for Complex Systems