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In this article, we propose a new sparse neural ordinary differential equation (ODE) model to characterize flexible relations among multiple functional processes. We characterize the latent states of the functions via a set of ODEs. We then model the dynamic changes of the latent states using a deep neural network (DNN) with a specially designed architecture and a sparsity‐inducing regularization. The new model is able to capture both nonlinear and sparse‐dependent relations among multivariate functions. We develop an efficient optimization algorithm to estimate the unknown weights for the DNN under the sparsity constraint. We establish both the algorithmic convergence and selection consistency, which constitute the theoretical guarantees of the proposed method. We illustrate the efficacy of the method through simulations and a gene regulatory network example. [ABSTRACT FROM AUTHOR]

The rapid growth of distributed energy resources integrated in distribution systems leads to an increasing need of continuously and automatically changing the system topology to realize the economic operation of distribution networks. This paper proposes an optimization model of dynamic reconfiguration for distribution networks based on a new method of time series analysis. Equivalent daily curve considering time‐varying nature of distributed generator and load demands is divided by an improved fuzzy C‐means clustering algorithm, where the indicator of section function is set to find the optimal reconfiguration time intervals. The uncertainty of distributed generator outputs and load demands is described by the interval algorithm. Then the affine Taylor expansion is adopted to solve the interval power flow equations. The reconfiguration optimization model is solved with decimal particle swarm optimization algorithm based on loop search. The optimal dynamic reconfiguration of a modified 70‐bus test system with distributed generators is carried out and the simulation results demonstrate the effectiveness and superiority of the proposed method. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]