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Abstract Deep generative learning cannot only be used for generating new data with statistical characteristics derived from input data but also for anomaly detection, by separating nominal and anomalous instances based on their reconstruction quality. In this paper, we explore the performance of three unsupervised deep generative models—variational autoencoders (VAEs) with Gaussian, Bernoulli, and Boltzmann priors—in detecting anomalies in multivariate time series of commercial-flight operations. We created two VAE models with discrete latent variables (DVAEs), one with a factorized Bernoulli prior and one with a restricted Boltzmann machine (RBM) with novel positive-phase architecture as prior, because of the demand for discrete-variable models in machine-learning applications and because the integration of quantum devices based on two-level quantum systems requires such models. To the best of our knowledge, our work is the first that applies DVAE models to anomaly-detection tasks in the aerospace field. The DVAE with RBM prior, using a relatively simple—and classically or quantum-mechanically enhanceable—sampling technique for the evolution of the RBM’s negative phase, performed better in detecting anomalies than the Bernoulli DVAE and on par with the Gaussian model, which has a continuous latent space. The transfer of a model to an unseen dataset with the same anomaly but without re-tuning of hyperparameters or re-training noticeably impaired anomaly-detection performance, but performance could be improved by post-training on the new dataset. The RBM model was robust to change of anomaly type and phase of flight during which the anomaly occurred. Our studies demonstrate the competitiveness of a discrete deep generative model with its Gaussian counterpart on anomaly-detection problems. Moreover, the DVAE model with RBM prior can be easily integrated with quantum sampling by outsourcing its generative process to measurements of quantum states obtained from a quantum annealer or gate-model device. 

Abstract System-level integration and optimization of food-energy-water systems (FEWS) require coordination of multiple agencies and decision-makers and incorporating their interdependence. In general, such coordination might be hard to achieve. As a result, the literature on FEWS management either optimizes the operations for one sector (or one decision-maker), or models interdependence among the sectors without optimizing their operations. In this article, we develop a novel multi-agent management optimization approach that is able to incorporate stochasticity and uncertainty in the system’s dynamics and interdependence of the water and energy resources for food production. The proposed method is the first attempt to utilize fundamentals of decision and game theories to optimize operations of multi-agent FEWS. We specifically focus on differentiating between (1) cooperative decision optimization of the operations, where all decision-makers cooperate to achieve the best outcome for the whole system, the social optimum, and (2) non-cooperative decision-making of the agents, the Nash equilibrium. Illustrating with a real-world case study of FEWS in Ventura County, California, we show the difference between the cooperative and non-cooperative decision making in terms of long-term expected cost of managing the system. We further show how the extra costs associated with utilizing the renewable sources of water and energy could be incentivised, so that the non-cooperative solution (the Nash equilibrium) would naturally converge to the best outcome for the whole system (the social optimum). 

Abstract Integrated management of food–energy–water systems (FEWS) requires a unified, flexible and reproducible approach to incorporate the interdependence between sectors, and include the risk of non-stationary environmental variations due to climate change. Most of the recently developed methods in the literature fall short of one or more aspects in such integration. In this article, we propose a novel approach based upon fundamentals of decision theory and reinforcement learning that (1) quantifies and propagates uncertainty, (2) incorporates resource interdependence, (3) includes the impact of uncontrolled variables such as climate variations, and (4) adaptively optimizes management decisions to minimize the costs and environmental impacts of crop production. Moreover, the proposed method is robust to problem-specific complexities and is easily reproducible. We illustrate the framework on a real-world case study in Ventura County, California.