Anticipating tipping in spatiotemporal systems with machine learning

TL;DR

This paper introduces a reservoir computing approach combined with non-negative matrix factorization to accurately predict the timing of critical tipping points in complex spatiotemporal systems, including climate models.

Contribution

It presents a novel framework that reduces data dimensionality and leverages reservoir computing to forecast tipping points with high accuracy and efficiency.

Findings

Successfully predicts tipping time within a narrow window across various systems.

Demonstrates robustness against common forecasting challenges.

Reduces computational overhead compared to full data processing.

Abstract

In nonlinear dynamical systems, tipping refers to a critical transition from one steady state to another, typically catastrophic, steady state, often resulting from a saddle-node bifurcation. Recently, the machine-learning framework of parameter-adaptable reservoir computing has been applied to predict tipping in systems described by low-dimensional stochastic differential equations. However, anticipating tipping in complex spatiotemporal dynamical systems remains a significant open problem. The ability to forecast not only the occurrence but also the precise timing of such tipping events is crucial for providing the actionable lead time necessary for timely mitigation. By utilizing the mathematical approach of non-negative matrix factorization to generate dimensionally reduced spatiotemporal data as input, we exploit parameter-adaptable reservoir computing to accurately anticipate tipping. We demonstrate that the tipping time can be identified within a narrow prediction window across a variety of spatiotemporal dynamical systems, as well as in CMIP5 (Coupled Model Intercomparison Project 5) climate projections. Furthermore, we show that this reservoir-computing framework, utilizing reduced input data, is robust against common forecasting challenges and significantly alleviates the computational overhead associated with processing full spatiotemporal data.