Forecasting sudden changes in complex systems is a critical but challenging task, with previously developed methods varying widely in their reliability. Here we develop a novel detection method, using simple theoretical models to train a deep neural network to detect critical transitions—the Early Warning Signal Network (EWSNet). We then demonstrate that this network, trained on simulated data, can reliably predict observed real-world transitions in systems ranging from rapid climatic change to the collapse of ecological populations. Importantly, our model appears to capture latent properties in time series missed by previous warning signals approaches, allowing us to not only detect if a transition is approaching, but critically whether the collapse will be catastrophic or non-catastrophic. These novel properties mean EWSNet has the potential to serve as an indicator of transitions across a broad spectrum of complex systems, without requiring information on the structure of the system being monitored. Our work highlights the practicality of deep learning for addressing further questions pertaining to ecosystem collapse and has much broader management implications.

Sudden transitions from one stable state to a contrasting state occur in complex systems ranging from the collapse of ecological populations to climatic change, with much recent work seeking to develop methods to predict these unexpected transitions from signals in time series data. However, previously developed methods vary widely in their reliability, and fail to classify whether an approaching collapse might be catastrophic (and hard to reverse) or non-catastrophic (easier to reverse) with significant implications for how such systems are managed. Here we develop a novel detection method, using simulated outcomes from a range of simple mathematical models with varying nonlinearity to train a deep neural network to detect critical transitions - the Early Warning Signal Network (EWSNet). We demonstrate that this neural network (EWSNet), trained on simulated data with minimal assumptions about the underlying structure of the system, can predict with high reliability observed real-world transitions in ecological and climatological data. Importantly, our model appears to capture latent properties in time series missed by previous warning signals approaches, allowing us to not only detect if a transition is approaching but critically whether the collapse will be catastrophic or non-catastrophic. The EWSNet can flag a critical transition with unprecedented accuracy, overcoming some of the major limitations of traditional methods based on phenomena such as Critical Slowing Down. These novel properties mean EWSNet has the potential to serve as a universal indicator of transitions across a broad spectrum of complex systems, without requiring information on the structure of the system being monitored. Our work highlights the practicality of deep learning for addressing further questions pertaining to ecosystem collapse and have much broader management implications.

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Normalizing flows provide an elegant approach to generative modeling that allows for efficient sampling and exact density evaluation of unknown data distributions. However, current techniques have significant limitations in their expressivity when the data distribution is supported on a lowdimensional manifold or has a non-trivial topology. We introduce a novel statistical framework for learning a mixture of local normalizing flows as "chart maps" over the data manifold. Our framework augments the expressivity of recent approaches while preserving the signature property of normalizing flows, that they admit exact density evaluation. We learn a suitable atlas of charts for the data manifold via a vector quantized autoencoder (VQ-AE) and the distributions over them using a conditional flow. We validate experimentally that our probabilistic framework enables existing approaches to better model data distributions over complex manifolds.