Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics

We live in a world of worry. Uncertainty is not new, but novel layers of uncertainties are interacting to create new kinds of uncertainty—a new uncertainty complex— never seen in human history.

There is a nagging sense that whatever control we have over our lives is slipping away, that the norms and institutions we used to rely on for stability and prosperity are not up to the task of today’s uncertainty complex.

One of the frustrating ironies of the Anthropocene is that while we have more power to influence our future, we do not necessarily have any more control over it.

Human Development Report 2021-2022

Complex systems, weather, climate, our own society and economy, can undergo “tipping point” transitions, suddenly changing their behavior dramatically and perhaps irreversibly, with little warning and potentially catastrophic consequences.

That’s why we need better ways to understand and anticipate the behaviour of complex systems, to mitigate the riske of unexpected undesirable lurking events.

Researchers are showing that machine learning algorithms can predict tipping-point transitions. This is a recent reference, with a (particularly) comprehensible and insightful abstract.

In this paper we consider the machine learning (ML) task of predicting tipping point transitions and long-term post-tipping-point behavior associated with the time evolution of an unknown (or partially unknown), non-stationary, potentially noisy and chaotic, dynamical system. We focus on the particularly challenging situation where the past dynamical state time series that is available for ML training predominantly lies in a restricted region of the state space, while the behavior to be predicted evolves on a larger state space set not fully observed by the ML model during training. In this situation, it is required that the ML prediction system have the ability to extrapolate to different dynamics past that which is observed during training. We investigate the extent to which ML methods are capable of accomplishing useful results for this task, as well as conditions under which they fail. In general, we found that the ML methods were surprisingly effective even in situations that were extremely challenging, but do (as one would expect) fail when “too much” extrapolation is required. For the latter case, we investigate the effectiveness of combining the ML approach with conventional modeling based on scientific knowledge, thus forming a hybrid prediction system which we find can enable useful prediction even when its ML-based and knowledge-based components fail when acting alone. We also found that achieving useful results may require using very carefully selected ML hyperparameters and we propose a hyperparameter optimization strategy to address this problem. The main conclusion of this paper is that ML-based approaches are promising tools for predicting the behavior of non-stationary dynamical systems even in the case where the future evolution (perhaps due to the crossing of a tipping point) includes dynamics on a set outside of that explored by the training data.

Patel, Dhruvit, and Edward Ott. ‘Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systems’. arXiv, 1 July 2022. https://doi.org/10.48550/arXiv.2207.00521.

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