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

TL;DR

The paper investigates neural Early Warning Signals (EWS) for spatially patterned phase transitions in dryland vegetation, using three lattice-based transition systems to generate training data. A CNN-LSTM classifier is trained on fourteen EWS indicators (spatial and temporal) to predict transitions and distinguish abrupt from continuous shifts, with careful data preparation and lead-time estimation. Results reveal that generalization across systems is variable and strongly dependent on the input indicators, with spatially oriented metrics such as subgraph centrality and patch-size distribution often providing better transfer in some cases. The work highlights the importance of diverse training data and cautions against over-interpreting transfer performance, while offering insights into how EWS information is encoded in complex spatiotemporal dynamics and guiding future development of robust, generalizable EWS tools for high-dimensional transitions.

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.

Figures (9)

• Figure 1: Snapshots from simulations of each spatiotemporal model undergoing a critical phase transition.
• Figure 2: Data processing workflow. Time series measurements from spatiotemporal models are dimensionally reduced by computing secondary statistics expected to encode information relevant to critical phenomena. Neural CNN-LSTM models are then trained on the resulting time series data for each of these EWS indicators, and tested on the corresponding statistic computed for the target test case.
• Figure 3: $F_1$ accuracies for neural classifiers trained on one or more of the three source systems and tested on withheld data from each model (computed across results for all EWS indicators)
• Figure 4: $F_1$ accuracy scores for all neural EWS models, separated by the statistical indicators on which they were trained. Performance is reported for tests carried out on simulations of the same system used to generate the training set (green) and for those on simulations of systems not included in training (blue). The black dotted line denotes the expected accuracy of a random classifier, as a baseline.
• Figure 5: Model classification accuracy as a function of time-to-transition. $F_1$ scores are computed across all models tested on withheld training data (blue) and transfer to new data sources (green). The shaded regions indicate the distributions of $F_1$ scores computed separately for each EWS indicator feature, with the solid lines denoting the median values. Time is measured in the arbitrary units of simulation steps.