1.6.1.5 Model methods

As well as statistical and network methods that look for changing dynamics in a system, more complex methods can predict movement towards tipping points. One example is a generalised model approach, which integrates knowledge about the system into models and may allow us to estimate, for example, changes in the leading eigenvalue of the system once small model assumptions have been made (Lade and Gross, 2012). System-specific indicators can also be derived where understanding about processes in the system can help us to assess its resilience in novel ways (Boulton et al., 2013).

Machine learning (ML) techniques are now being applied to tipping point prediction. The documented success of neural networks for time series classification problems has inspired the development of similar ML methods specifically for EWS detection. There is a natural synergy to this approach in that the same CSD phenomena manifest across a wide range of systems approaching critical transitions, so the notoriously data-intensive task of training a neural network can be accomplished using plentiful synthetic data and still produce a result which can be applied to observational data (which is often more scarce and harder to label).

Deep learning models (which combine convolutional neural network layers with recurrent Long Short-Term Memory modules) have shown promise for EWS detection, outperforming methods using traditional statistical indicators (variance, AR(1), etc.) on a variety of test cases both real and simulated (Bury et al., 2021; Deb et. al., 2021). Furthermore, these models have exhibited success in inferring the type of oncoming bifurcation from observed pre-transition dynamics, and have performed well on rapid transitions in simple spatial models that evolve over time (Dylewsky et al., 2023).

Other ML techniques can also tell us something about how far systems are from tipping. For example, the ‘random forest’ method could be used to determine the factors that determine the AR(1) value in different areas of vegetation, and thus how close to tipping these areas could be, based on driving variables (Forzieri et al., 2022). Combining traditional EWS and ML techniques could provide some of the best prospects for monitoring systems that may be approaching tipping.