Direct estimation of prediction intervals for solar and wind regional energy forecasting with deep neural networks

Abstract

Deep neural networks (DNN) are becoming increasingly relevant for probabilistic forecasting because of their ability to estimate prediction intervals (PIs). Two different ways for estimating PIs with neural networks stand out: quantile estimation for posterior PI construction and direct PI estimation. The former first estimates quantiles, which are then used to construct PIs, while the latter directly obtains the lower and upper PI bounds by optimizing some loss functions, with the advantage that PI width is directly considered in the optimization process and thus may result in narrower intervals. In this work, two different DNN-based models are studied for direct PI estimation, and compared with DNN for quantile estimation in the context of solar and wind regional energy forecasting. The first approach is based on the recent quality-driven loss and is formulated to estimate multiple PIs with a single model. The second is a novel approach that employs hypernetworks (HN), where direct PI estimation is formulated as a multi-objective problem, returning a Pareto front of solutions that contains all possible coverage-width optimal trade-offs. This formulation allows HN to obtain optimal PIs for all possible coverages without increasing the number of network outputs or adjusting additional hyperparameters, as opposed to the first direct model. Results show that prediction intervals from direct estimation are narrower (up to 20%) than those of quantile estimation, for target coverages 70%–80% for all regions, and also 85%, 90%, and 95% depending on the region, while HN always achieves the required coverage for the higher target coverages.