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Assessing set-membership and evaluating distances to the related set boundary are problems of widespread interest, and can often be computationally challenging. Seeking efficient learning models for such tasks, this paper deals with voltage stability margin prediction for power systems. Supervised training of such models is conventionally hard due to high-dimensional feature space, and a cumbersome label-generation process. Nevertheless, one may find related easy auxiliary tasks, such as voltage stability verification, that can aid in training for the hard task. This paper develops a novel approach for such settings by leveraging transfer learning. A Gaussian process-based learning model is efficiently trained using learning- and physics-based auxiliary tasks. Numerical tests demonstrate markedly improved performance that is harnessed alongside the benefit of uncertainty quantification to suit the needs of the considered application. 

The critical role of gas fired-plants to compensate renewable generation has increased the operational variability in natural gas networks (GN). Towards developing more reliable and efficient computational tools for GN monitoring, control, and planning, this work considers the task of solving the nonlinear equations governing steady-state flows and pressures in GNs. It is first shown that if the gas flow equations are feasible, they enjoy a unique solution. To the best of our knowledge, this is the first result proving uniqueness of the steady-state gas flow solution over the entire feasible domain of gas injections. To find this solution, we put forth a mixed-integer second-order cone program (MI-SOCP)-based solver relying on a relaxation of the gas flow equations. This relaxation is provably exact under specific network topologies. Unlike existing alternatives, the devised solver does not need proper initialization or knowing the gas flow directions beforehand, and can handle gas networks with compressors. Numerical tests on tree and meshed networks indicate that the relaxation is exact even when the derived conditions are not met.