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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. 

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. 

The widespread use of distributed energy sources (DERs) raises significant challenges for power system design, planning, and operation, leading to wide adaptation of tools on hosting capacity analysis (HCA). Traditional HCA methods conduct extensive power flow analysis. Due to the computation burden, these time-consuming methods fail to provide online hosting capacity (HC) in large distribution systems. To solve the problem, we first propose a deep learning-based problem formulation for HCA, which conducts offline training and determines HC in real time. The used learning model, long short-term memory (LSTM), implements historical time-series data to capture periodical patterns in distribution systems. However, directly applying LSTMs suffers from low accuracy due to the lack of consideration on spatial information, where location information like feeder topology is critical in nodal HCA. Therefore, we modify the forget gate function to dual forget gates, to capture the spatial correlation within the grid. Such a design turns the LSTM into the Spatial-Temporal LSTM (ST-LSTM). Moreover, as voltage violations are the most vital constraints in HCA, we design a voltage sensitivity gate to increase accuracy further. The results of LSTMs and ST-LSTMs on feeders, such as IEEE 34-, 123-bus feeders, and utility feeders, validate our designs.