Probabilistic indoor temperature forecasting: A new approach using bernstein-polynomial normalizing flows

Abstract

Numerous studies have demonstrated that energy demand in the building sector, particularly for heating, ventilation, and air conditioning systems, can be reduced by forecasting future indoor temperatures and applying targeted control strategies. Accurate indoor temperature forecasts depend on understanding random variables such as occupancy and the number of active electrical devices. However, detecting these random influences is challenging, leading existing methods to be overly specific, reliant on expensive sensors, and poorly generalizable across different buildings. Moreover, prevalent point forecasting methods fail to account for the uncertainty surrounding future outcomes. In this paper, we propose that instead of attempting to eliminate naturally occurring random disturbances, it is more effective to incorporate these uncertainties into the modeling process. We introduce a deep learning methodology for probabilistic forecasting that predicts future temperatures as a probability distribution, integrating the inherent randomness of the data without requiring direct measurements. The proposed model is based on normalizing flows with flexible Bernstein polynomials and is compared to a Gaussian baseline. This approach enables the estimation of complex distributions via the maximum likelihood principle, with only mild assumptions on its shape. Due to the lack of high-quality real-world data, we use simulated data from various rooms with differing characteristics and evaluate both models in terms of robustness and flexibility. Our results indicate that our model accurately predicts indoor temperature distributions and generalizes well to different and previously unseen rooms. The dataset and code are published along with this paper, to provide reproducible results and benchmark data to the community.