Learning from the past: predicting critical transitions with machine learning trained on surrogates of historical data

Complex systems can undergo critical transitions, where slowly changing environmental conditions trigger a sudden shift to a new, potentially catastrophic state. Early warning signals for these events are crucial for decision-making in fields such as ecology, biology and climate science. Generic early warning signals motivated by dynamical systems theory have had mixed success on real noisy data. More recent studies found that deep learning classifiers trained on synthetic data could improve performance. However, neither of these methods take advantage of historical, system-specific data. Here, we introduce an approach that trains machine learning classifiers directly on surrogate data of past transitions, namely surrogate data-based machine learning (SDML). The approach provides early warning signals in empirical and experimental data from geology, climatology, sociology, and cardiology with higher sensitivity and specificity than two widely used generic early warning signals -- variance and lag-1 autocorrelation. Since the approach is trained directly on surrogates of historical data, it is not bound by the restricting assumption of a local bifurcation like previous methods. This system-specific approach can contribute to improved early warning signals to help humans better prepare for or avoid undesirable critical transitions.

Predicting discrete-time bifurcations with deep learning

Many natural and man-made systems are prone to critical transitions -- abrupt and potentially devastating changes in dynamics. Deep learning classifiers can provide an early warning signal (EWS) for critical transitions by learning generic features of bifurcations (dynamical instabilities) from large simulated training data sets. So far, classifiers have only been trained to predict continuous-time bifurcations, ignoring rich dynamics unique to discrete-time bifurcations. Here, we train a deep learning classifier to provide an EWS for the five local discrete-time bifurcations of codimension-1. We test the classifier on simulation data from discrete-time models used in physiology, economics and ecology, as well as experimental data of spontaneously beating chick-heart aggregates that undergo a period-doubling bifurcation. The classifier outperforms commonly used EWS under a wide range of noise intensities and rates of approach to the bifurcation. It also predicts the correct bifurcation in most cases, with particularly high accuracy for the period-doubling, Neimark-Sacker and fold bifurcations. Deep learning as a tool for bifurcation prediction is still in its nascence and has the potential to transform the way we monitor systems for critical transitions.

Universal Early Warning Signals of Phase Transitions in Climate Systems

The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and potentially irreversible shift is well established, but prediction of these events using standard forecast modeling techniques is quite difficult. This has led to the development of an alternative suite of methods that seek to identify signatures of critical phenomena in data, which are expected to occur in advance of many classes of dynamical bifurcation. Crucially, the manifestations of these critical phenomena are generic across a variety of systems, meaning that data-intensive deep learning methods can be trained on (abundant) synthetic data and plausibly prove effective when transferred to (more limited) empirical data sets. This paper provides a proof of concept for this approach as applied to lattice phase transitions: a deep neural network trained exclusively on 2D Ising model phase transitions is tested on a number of real and simulated climate systems with considerable success. Its accuracy frequently surpasses that of conventional statistical indicators, with performance shown to be consistently improved by the inclusion of spatial indicators. Tools such as this may offer valuable insight into climate tipping events, as remote sensing measurements provide increasingly abundant data on complex geospatially-resolved Earth systems.