Joint probabilistic forecasting of electricity and heat demand in residential buildings using LSTM and weather-driven features
Forecasting energy demand is critical to resource optimization, grid operation, and sustainability for smart buildings and urban energy systems. This study presents a probabilistic forecasting framework designed to jointly predict hourly electricity and heat demand for a residential building using deep learning. The model ingests hourly multivariate data spanning multiple years, comprising two energy targets — electricity and heat demand — and five weather covariates — air temperature, relative humidity, wind speed, solar irradiation, and air pressure — all of which are known to significantly influence building energy consumption. The proposed framework is based on a Long Short-Term Memory (LSTM) neural network trained using look-back windows of 48 h. Performance is evaluated using Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). The proposed LSTM-based framework achieves strong forecasting accuracy, with a 1-hour horizon yielding MAE = 157.7 kW and RMSE = 218.4 kW for electricity, and MAE = 128.0 kW and RMSE = 184.8 kW for heat. Even for 720-hour forecasts, errors remain low, and the uncertainty intervals are well-calibrated (Mean Prediction Interval Width (MPIW) ≈ 308–377 kW, Prediction Interval Normalized Average Width (PINAW) ≈ 0.20–0.25). Ablation experiments highlight the significance of interpolation, normalization, cyclic encoding, and weather features, while SHapley Additive exPlanations (SHAP)-based explainability provides interpretable insights into energy demand behaviour. Comprehensive benchmark evaluation against Persistence, Linear Regression (LR), Vector Autoregression (VAR), and Quantile Regression (QR) baselines confirms superior probabilistic performance (Continuous Ranked Probability Score (CRPS) improvement of 21.6% for electricity, 22.9% for heat; Energy Score (ES) improvement of 16.1%; Variogram Score (VS) improvement of 16.8%). An empirical comparison between the proposed joint model and two independent LSTMs validates the joint architecture through a 21.4% Variogram Score improvement and 12.8% Energy Score improvement.