In recent years, researchers proposed a variety of deep learning models for wind power forecasting. These models predict the wind power generation of wind farms or entire regions more accurately than traditional machine learning algorithms or physical models. However, latest research has shown that deep learning models can often be manipulated by adversarial attacks. Since wind power forecasts are essential for the stability of modern power systems, it is important to protect them from this threat. In this work, we investigate the vulnerability of two different forecasting models to targeted, semi-targeted, and untargeted adversarial attacks. We consider a Long Short-Term Memory (LSTM) network for predicting the power generation of individual wind farms and a Convolutional Neural Network (CNN) for forecasting the wind power generation throughout Germany. Moreover, we propose the Total Adversarial Robustness Score (TARS), an evaluation metric for quantifying the robustness of regression models to targeted and semi-targeted adversarial attacks. It assesses the impact of attacks on the model's performance, as well as the extent to which the attacker's goal was achieved, by assigning a score between 0 (very vulnerable) and 1 (very robust). In our experiments, the LSTM forecasting model was fairly robust and achieved a TARS value of over 0.78 for all adversarial attacks investigated. The CNN forecasting model only achieved TARS values below 0.10 when trained ordinarily, and was thus very vulnerable. Yet, its robustness could be significantly improved by adversarial training, which always resulted in a TARS above 0.46.

In this article, we present a novel approach to multivariate probabilistic forecasting. Our approach is based on an extension of single-output quantile regression (QR) to multivariate-targets, called quantile surfaces (QS). QS uses a simple yet compelling idea of indexing observations of a probabilistic forecast through direction and vector length to estimate a central tendency. We extend the single-output QR technique to multivariate probabilistic targets. QS efficiently models dependencies in multivariate target variables and represents probability distributions through discrete quantile levels. Therefore, we present a novel two-stage process. In the first stage, we perform a deterministic point forecast (i.e., central tendency estimation). Subsequently, we model the prediction uncertainty using QS involving neural networks called quantile surface regression neural networks (QSNN). Additionally, we introduce new methods for efficient and straightforward evaluation of the reliability and sharpness of the issued probabilistic QS predictions. We complement this by the directional extension of the Continuous Ranked Probability Score (CRPS) score. Finally, we evaluate our novel approach on synthetic data and two currently researched real-world challenges in two different domains: First, probabilistic forecasting for renewable energy power generation, second, short-term cyclists trajectory forecasting for autonomously driving vehicles. Especially for the latter, our empirical results show that even a simple one-layer QSNN outperforms traditional parametric multivariate forecasting techniques, thus improving the state-of-the-art performance.