# Ultra-Early Prediction of Tipping Points: Integrating Dynamical Measures with Reservoir Computing

arXiv: https://arxiv.org/abs/2603.14944 · HTML: https://mlsanity.com/paper/2603.14944/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 61 references that are in the map.
- First posted on arXiv 16 Mar 2026.

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

- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [Machine learning prediction of critical transition and system collapse](https://mlsanity.com/paper/2012.01545/) (2020)
- [A Systematic Exploration of Reservoir Computing for Forecasting Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/2201.08910/) (2022)
- [Do Reservoir Computers Work Best at the Edge of Chaos?](https://mlsanity.com/paper/2012.01409/) (2020)

## Built on by (most cited first, 2 of 2)

- [In-context learning to predict critical transitions in dynamical systems](https://mlsanity.com/paper/2605.12308/) (2026)
- [Rank Collapse Is Recoverable, Growing |Q| Is Not: Out-of-Sample Early Warning for Value Divergence in High-UTD Soft Actor-Critic](https://mlsanity.com/paper/2609.32819/) (2026)

## Abstract (arXiv)

Complex dynamical systems-such as climate, ecosystems, and economics-can undergo catastrophic and potentially irreversible regime changes, often triggered by environmental parameter drift and stochastic disturbances. These critical thresholds, known as tipping points, pose a prediction problem of both theoretical and practical significance, yet remain largely unresolved. To address this, we articulate a model-free framework that integrates the measures characterizing the stability and sensitivity of dynamical systems with the reservoir computing (RC), a lightweight machine learning technique, using only observational time series data. The framework consists of two stages. The first stage involves using RC to robustly learn local complex dynamics from observational data segmented into windows. The second stage focuses on accurately detecting early warning signals of tipping points by analyzing the learned autonomous RC dynamics through dynamical measures, including the dominant eigenvalue of the Jacobian matrix, the maximum Floquet multiplier, and the maximum Lyapunov exponent. Furthermore, when these dynamical measures exhibit trend-like patterns, their extrapolation enables ultra-early prediction of tipping points significantly prior to the occurrence of critical transitions. We conduct a rigorous theoretical analysis of the proposed method and perform extensive numerical evaluations on a series of representative synthetic systems and eight real-world datasets, as well as quantitatively predict the tipping time of the Atlantic Meridional Overturning Circulation system. Experimental results demonstrate that our framework exhibits advantages over the baselines in comprehensive evaluations, particularly in terms of dynamical interpretability, prediction stability and robustness, and ultra-early prediction capability.