F.J.G. Silva

Luis Briceño-Arias, Dante Kalise, Ziad Kobeissi et al.

We study a numerical approximation of a time-dependent Mean Field Game (MFG) system with local couplings. The discretization we consider stems from a variational approach described in [Briceno-Arias, Kalise, and Silva, SIAM J. Control Optim., 2017] for the stationary problem and leads to the finite difference scheme introduced by Achdou and Capuzzo-Dolcetta in [SIAM J. Numer. Anal., 48(3):1136-1162, 2010]. In order to solve the finite dimensional variational problems, in [Briceno-Arias, Kalise, and Silva, SIAM J. Control Optim., 2017] the authors implement the primal-dual algorithm introduced by Chambolle and Pock in [J. Math. Imaging Vision, 40(1):120-145, 2011], whose core consists in iteratively solving linear systems and applying a proximity operator. We apply that method to time-dependent MFG and, for large viscosity parameters, we improve the linear system solution by replacing the direct approach used in [Briceno-Arias, Kalise, and Silva, SIAM J. Control Optim., 2017] by suitable preconditioned iterative algorithms.

Sotiris Pelekis, Evangelos Karakolis, Francisco Silva et al.

In power grids, short-term load forecasting (STLF) is crucial as it contributes to the optimization of their reliability, emissions, and costs, while it enables the participation of energy companies in the energy market. STLF is a challenging task, due to the complex demand of active and reactive power from multiple types of electrical loads and their dependence on numerous exogenous variables. Amongst them, special circumstances, such as the COVID-19 pandemic, can often be the reason behind distribution shifts of load series. This work conducts a comparative study of Deep Learning (DL) architectures, namely Neural Basis Expansion Analysis Time Series Forecasting (N-BEATS), Long Short-Term Memory (LSTM), and Temporal Convolutional Networks (TCN), with respect to forecasting accuracy and training sustainability, meanwhile examining their out-of-distribution generalization capabilities during the COVID-19 pandemic era. A Pattern Sequence Forecasting (PSF) model is used as baseline. The case study focuses on day-ahead forecasts for the Portuguese national 15-minute resolution net load time series. The results can be leveraged by energy companies and network operators (i) to reinforce their forecasting toolkit with state-of-the-art DL models; (ii) to become aware of the serious consequences of crisis events on model performance; (iii) as a high-level model evaluation, deployment, and sustainability guide within a smart grid context.

Francisco Silva, Mikel Sanz, João Seixas et al.

Memristors, resistors with memory whose outputs depend on the history of their inputs, have been used with success in neuromorphic architectures, particularly as synapses and non-volatile memories. However, to the best of our knowledge, no model for a network in which both the synapses and the neurons are implemented using memristors has been proposed so far. In the present work we introduce models for single and multilayer perceptrons based exclusively on memristors. We adapt the delta rule to the memristor-based single-layer perceptron and the backpropagation algorithm to the memristor-based multilayer perceptron. Our results show that both perform as expected for perceptrons, including satisfying Minsky-Papert's theorem. As a consequence of the Universal Approximation Theorem, they also show that memristors are universal function approximators. By using memristors for both the neurons and the synapses, our models pave the way for novel memristor-based neural network architectures and algorithms. A neural network based on memristors could show advantages in terms of energy conservation and open up possibilities for other learning systems to be adapted to a memristor-based paradigm, both in the classical and quantum learning realms.