# Extrapolating tipping points and simulating non-stationary dynamics of complex systems using efficient machine learning

arXiv: https://arxiv.org/abs/2312.06283 · HTML: https://mlsanity.com/paper/2312.06283/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 30 references that are in the map.
- First posted on arXiv 11 Dec 2023.

## Builds on (most cited first, 10 of 10)

- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Machine learning prediction of critical transition and system collapse](https://mlsanity.com/paper/2012.01545/) (2020)
- [Will Artificial Intelligence supersede Earth System and Climate Models?](https://mlsanity.com/paper/2101.09126/) (2021)
- [Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systems](https://mlsanity.com/paper/2207.00521/) (2022)
- [Multifunctionality in a Reservoir Computer](https://mlsanity.com/paper/2008.06348/) (2020)
- [Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computing](https://mlsanity.com/paper/2203.13294/) (2022)
- [Learning unseen coexisting attractors](https://mlsanity.com/paper/2207.14133/) (2022)
- [Accuracy of neural networks for the simulation of chaotic dynamics: precision of training data vs precision of the algorithm](https://mlsanity.com/paper/2008.04222/) (2020)
- [Exploring the limits of multifunctionality across different reservoir computers](https://mlsanity.com/paper/2205.11375/) (2022)
- [Controlling dynamical systems to complex target states using machine learning: next-generation vs. classical reservoir computing](https://mlsanity.com/paper/2307.07195/) (2023)

## Built on by (most cited first, 9 of 9)

- [Confabulation dynamics in a reservoir computer: Filling in the gaps with untrained attractors](https://mlsanity.com/paper/2505.04792/) (2025)
- [Position: A Dynamical Systems Perspective is Needed to Advance Time Series Modeling](https://mlsanity.com/paper/2602.16864/) (2026)
- [Tailored Forecasting from Short Time Series via Meta-learning](https://mlsanity.com/paper/2501.16325/) (2025)
- [Controlling Dynamical Systems into Unseen Target States Using Machine Learning](https://mlsanity.com/paper/2412.10251/) (2024)
- [Deep Learning Surrogates for Emulating Stochastic Climate Tipping Dynamics](https://mlsanity.com/paper/2605.20580/) (2026)
- [Flow map learning in nonlinear vector autoregressive models: influence of the feature-library structure on the training error](https://mlsanity.com/paper/2605.31438/) (2026)
- [Topological Out-of-Domain Generalization in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2606.22969/) (2026)
- [Extrapolating the emergence of Hamiltonian chaos with random-feature Hamiltonian neural networks](https://mlsanity.com/paper/2607.28977/) (2026)
- [Learning Chaos Without Seeing Chaos: Extrapolation of Global Dynamics in Autoregressive Transformers](https://mlsanity.com/paper/2609.38814/) (2026)

## Abstract (arXiv)

Model-free and data-driven prediction of tipping point transitions in nonlinear dynamical systems is a challenging and outstanding task in complex systems science. We propose a novel, fully data-driven machine learning algorithm based on next-generation reservoir computing to extrapolate the bifurcation behavior of nonlinear dynamical systems using stationary training data samples. We show that this method can extrapolate tipping point transitions. Furthermore, it is demonstrated that the trained next-generation reservoir computing architecture can be used to predict non-stationary dynamics with time-varying bifurcation parameters. In doing so, post-tipping point dynamics of unseen parameter regions can be simulated.