Abstract

This work proposes a new methodology for the construction of deep learning-based prediction intervals (PIs) based on a selective jointly supervised cost function. The proposed method aims to preserve the advantages of the traditional joint supervision method, such as its interval robustness and compatibility with gradient-based optimizers, while improving the general convergence of the utilized training algorithms and reducing the computational costs incurred when using deep learning models. To test the capability of the proposed method to estimate uncertainties in complex, nonlinear dynamic systems, two prediction interval construction experiments were tested: one with an artificially generated dataset consisting of a modified Chen series and another using real electrical load data measured in the Huatacondo Microgrid in northern Chile. In these experiments, the proposed model was required to generate future predictions with accompanying prediction intervals, while its performance was measured according to its interval coverage, average width, average prediction error and computational cost of training. The proposal's performance was compared with that of two other state-of-the-art interval models: the quality-driven method (Pearce et al. 2018), and the traditional joint supervision method (Cruz et al. 2018). The experimental results showed that the proposed selective joint supervision method incurred lower computational costs than the traditional joint supervision approach, with training times reduction magnitudes ranging from 15% to 85%. Additionally, the results showed that the proposed selective joint supervision method achieved better interval performance when using deep learning-based network architectures, showing up to a 6% prediction error decrease and up to a 15% overall interval width decrease.