Neural models for prediction of spatially patterned phase transitions: methods and challenges

TL;DR

This paper investigates the use of neural networks for predicting spatially patterned phase transitions in dryland ecosystems, highlighting their potential and limitations in generalizing from synthetic to real-world data.

Contribution

It provides a critical assessment of neural early warning signals for complex spatial phase transitions and explores how these models encode predictive information.

Findings

Model performance varies significantly when training and testing data sources are interchanged.

Neural models can distinguish between abrupt and continuous transitions.

Insights into the encoding of EWS information in spatiotemporal dynamics are gained.

Abstract

Dryland vegetation ecosystems are known to be susceptible to critical transitions between alternative stable states when subjected to external forcing. Such transitions are often discussed through the framework of bifurcation theory, but the spatial patterning of vegetation, which is characteristic of drylands, leads to dynamics that are much more complex and diverse than local bifurcations. Recent methodological developments in Early Warning Signal (EWS) detection have shown promise in identifying dynamical signatures of oncoming critical transitions, with particularly strong predictive capabilities being demonstrated by deep neural networks. However, a machine learning model trained on synthetic examples is only useful if it can effectively transfer to a test case of practical interest. These models' capacity to generalize in this manner has been demonstrated for bifurcation transitions, but it is not as well characterized for high-dimensional phase transitions. This paper explores the successes and shortcomings of neural EWS detection for spatially patterned phase transitions, and shows how these models can be used to gain insight into where and how EWS-relevant information is encoded in spatiotemporal dynamics. A few paradigmatic test systems are used to illustrate how the capabilities of such models can be probed in a number of ways, with particular attention to the performances of a number of proposed statistical indicators for EWS and to the supplementary task of distinguishing between abrupt and continuous transitions. Results reveal that model performance often changes dramatically when training and test data sources are interchanged, which offers new insight into the criteria for model generalization.