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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. 

Abstract This article presents an extremum‐seeking control (ESC) algorithm for unmodeled nonlinear systems with known steady‐state gain and generally non‐convex cost functions with bounded curvature. The main contribution of this article is a novel gradient estimator, which uses a polyhedral set that characterizes all gradient estimates consistent with the collected data. The gradient estimator is posed as a quadratic program, which selects the gradient estimate that provides the best worst‐case convergence of the closed‐loop Lyapunov function. We show that the polyhedral‐based gradient estimator ensures the stability of the closed‐loop system formed by the plant and optimization algorithm. Furthermore, the estimated gradient provably produces the optimal robust convergence. We demonstrate our ESC controller through three benchmark examples and one practical example, which shows our ESC has fast and robust convergence to the optimal equilibrium. 

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.