Use of artificial neural networks as explicit finite difference operators

Results of a numerical exercise, substituting a numerical operator by an artificial neural network (ANN) are presented in this paper. The numerical operator used is the explicit form of the finite difference (FD) scheme. The FD scheme was used to discretize the one-dimensional transport equation, which included both the advection and dispersion terms. Inputs to the ANN are the FD representation of the transport equation, and the concentration was designated as the output. Concentration values used for training the ANN were obtained from analytical solutions. The numerical operator was reconstructed from a back calculation of the weights of the ANN. Linear transfer functions were used for this purpose. The ANN was able to accurately recover the velocity used in the training data, but not the dispersion coefficient. This capability was improved when numerical dispersion was taken into account; however, it is limited to the condition: C/P<0.5 , where C is the Courant number and P , the Peclet number (i.e., the restriction imposed by the Neumann stability condition).

GTES: An optimized game-theoretic demand-side management scheme for smart grid

Demand-side management in smart grids has emerged as a hot topic for optimizing energy consumption. In conventional research works, energy consumption is optimized from the perspective of either the users or the power company. In this paper, we investigate how energy consumption may be optimized by taking into consideration the interaction between both parties. We propose a new energy price model as a function of total energy consumption. Also, we propose a new objective function, which optimizes the difference between the value and cost of energy. The power supplier pulls consumers in a round-robin fashion and provides them with energy price parameter and current consumption summary vector. Each user then optimizes his own schedule and reports it to the supplier, which, in turn, updates its energy price parameter before pulling the next consumers. This interaction between the power company and its consumers is modeled through a two-step centralized game, based on which we propose our game-theoretic energy schedule (GTES) method. The objective of our GTES method is to reduce the peak-to-average power ratio by optimizing the users' energy schedules. The performance of the GTES approach is evaluated through computer-based simulations. © 2014 IEEE.