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Abstract Identifying and understanding various causal relations are fundamental to climate dynamics for improving the predictive capacity of Earth system modeling. In particular, causality in Earth systems has manifest temporal periodicities, like physical climate variabilities. To unravel the characteristic frequency of causality in climate dynamics, we develop a data‐analytic framework based on a combination of causality detection and Hilbert spectral analysis, using a long‐term temperature and precipitation dataset in the contiguous United States. Using the Huang–Hilbert transform, we identify the intrinsic frequencies of cross‐regional causality for precipitation and temperature, ranging from interannual to interdecadal time scales. In addition, we analyze the spectra of the physical climate variabilities, including El Niño‐Southern Oscillation and Pacific Decadal Oscillation. It is found that the intrinsic causal frequencies are positively associated with the physics of the oscillations in the global climate system. The proposed methodology provides fresh insights into the causal connectivity in Earth's hydroclimatic system and its underlying mechanism as regulated by the characteristic low‐frequency variability associated with various climatic dynamics. 

The Atlantic Meridional Overturning Circulation (AMOC) is a significant component of the global ocean system, which has so far ensured a relatively warm climate for the North Atlantic and mild conditions in regions, such as Western Europe. The AMOC is also critical for the global climate. The complexity of the dynamical system underlying the AMOC is so vast that a long-term assessment of the potential risk of AMOC collapse is extremely challenging. However, short-term prediction can lead to accurate estimates of the dynamical state of the AMOC and possibly to early warning signals for guiding policy making and control strategies toward preventing AMOC collapse in the long term. We develop a model-free, machine-learning framework to predict the AMOC dynamical state in the short term by employing five datasets: MOVE and RAPID (observational), AMOC fingerprint (proxy records), and AMOC simulated fingerprint and CESM AMOC (synthetic). We demonstrate the power of our framework in predicting the variability of the AMOC within the maximum prediction horizon of 12 or 24 months. A number of issues affecting the prediction performance are investigated. 

Reinforcement learning (RL) has been employed to devise the best course of actions in defending the critical infrastructures, such as power networks against cyberattacks. Nonetheless, even in the case of the smallest power grids, the action space of RL experiences exponential growth, rendering efficient exploration by the RL agent practically unattainable. The current RL algorithms tailored to power grids are generally not suited when the state-action space size becomes large, despite trade-offs. We address the large action-space problem for power grid security by exploiting temporal graph convolutional neural networks (TGCNs) to develop a parallel but heterogeneous RL framework. In particular, we divide the action space into smaller subspaces, each explored by an RL agent. How to efficiently organize the spatiotemporal action sequences then becomes a great challenge. We invoke TGCN to meet this challenge by accurately predicting the performance of each individual RL agent in the event of an attack. The top performing agent is selected, resulting in the optimal sequence of actions. First, we investigate the action-space size comparison for IEEE 5-bus and 14-bus systems. Furthermore, we use IEEE 14-bus and IEEE 118-bus systems coupled with the Grid2Op platform to illustrate the performance and action division influence on training times and grid survival rates using both deep Q-learning and Soft Actor Critic trained agents and Grid2Op default greedy agents. Our TGCN framework provides a computationally reasonable approach for generating the best course of actions to defend cyber physical systems against attacks. 

Abstract Global climate change has been shown to cause longer, more intense, and frequent heatwaves, of which anthropogenic stressors concentrated in urban areas are a critical contributor. In this study, we investigate the causal interactions during heatwaves across 520 urban sites in the U.S. combining complex network and causal analysis. The presence of regional mediators is manifest in the constructed causal networks, together with long-range teleconnections. More importantly, megacities, such as New York City and Chicago, are causally connected with most of other cities and mediate the structure of urban networks during heatwaves. We also identified a significantly positive correlation between the causality strength and the total populations in megacities. These findings corroborate the contribution of human activities e.g., anthropogenic emissions of greenhouse gases or waste heat, to urban heatwaves. The emergence of teleconnections and supernodes are informative for the prediction and adaptation to heatwaves under global climate change. 

We articulate the design imperatives for machine learning based digital twins for nonlinear dynamical systems, which can be used to monitor the “health” of the system and anticipate future collapse. The fundamental requirement for digital twins of nonlinear dynamical systems is dynamical evolution: the digital twin must be able to evolve its dynamical state at the present time to the next time step without further state input—a requirement that reservoir computing naturally meets. We conduct extensive tests using prototypical systems from optics, ecology, and climate, where the respective specific examples are a chaotic CO2 laser system, a model of phytoplankton subject to seasonality, and the Lorenz-96 climate network. We demonstrate that, with a single or parallel reservoir computer, the digital twins are capable of a variety of challenging forecasting and monitoring tasks. Our digital twin has the following capabilities: (1) extrapolating the dynamics of the target system to predict how it may respond to a changing dynamical environment, e.g., a driving signal that it has never experienced before, (2) making continual forecasting and monitoring with sparse real-time updates under non-stationary external driving, (3) inferring hidden variables in the target system and accurately reproducing/predicting their dynamical evolution, (4) adapting to external driving of different waveform, and (5) extrapolating the global bifurcation behaviors to network systems of different sizes. These features make our digital twins appealing in applications, such as monitoring the health of critical systems and forecasting their potential collapse induced by environmental changes or perturbations. Such systems can be an infrastructure, an ecosystem, or a regional climate system. 

Data-based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to science, engineering, and beyond. Inspired by the widely used methodology in recent years, the cross-map-based techniques, we develop a general framework to advance towards a comprehensive understanding of dynamical causal mechanisms, which is consistent with the natural interpretation of causality. In particular, instead of measuring the smoothness of the cross-map as conventionally implemented, we define causation through measuring the scaling law for the continuity of the investigated dynamical system directly. The uncovered scaling law enables accurate, reliable, and efficient detection of causation and assessment of its strength in general complex dynamical systems, outperforming those existing representative methods. The continuity scaling-based framework is rigorously established and demonstrated using datasets from model complex systems and the real world. 

There is a growing recognition that ecological systems can spend extended periods of time far away from an asymptotic state, and that ecological understanding will therefore require a deeper appreciation for how long ecological transients arise. Recent work has defined classes of deterministic mechanisms that can lead to long transients. Given the ubiquity of stochasticity in ecological systems, a similar systematic treatment of transients that includes the influence of stochasticity is important. Stochasticity can of course promote the appearance of transient dynamics by preventing systems from settling permanently near their asymptotic state, but stochasticity also interacts with deterministic features to create qualitatively new dynamics. As such, stochasticity may shorten, extend or fundamentally change a system’s transient dynamics. Here, we describe a general framework that is developing for understanding the range of possible outcomes when random processes impact the dynamics of ecological systems over realistic time scales. We emphasize that we can understand the ways in which stochasticity can either extend or reduce the lifetime of transients by studying the interactions between the stochastic and deterministic processes present, and we summarize both the current state of knowledge and avenues for future advances.