Performance Evaluation of Machine Learning Models for Multi-Output Building Energy Prediction

Full abstract

Read the full abstract

Accurate prediction of building heating and cooling loads is central to energy-efficient design, and because these loads are strongly correlated, they represent a suitable multi-output regression problem. This study compares six models from three families—linear (Linear Regression, Polynomial Regression), kernel-based (Support Vector Regression, Kernel Ridge Regression), and gradient-boosting ensembles (XGBoost, LightGBM)—for predicting the heating (y1) and cooling (y2) loads, and additionally evaluates a joint neural network (Joint NN) that predicts both outputs together. The models were assessed on the publicly available Energy Performance of Buildings dataset, comprising 768 samples with eight input variables and two highly correlated outputs (r = 0.98). Performance was measured by mean absolute error (MAE), mean relative error (MRE), and mean squared error (MSE) using 10-fold cross-validation repeated 100 times, reported as mean ± standard deviation. LightGBM achieved the lowest error on both outputs (MAE = 0.0077 ± 0.0009 for heating and 0.0173 ± 0.0022 for cooling), reducing MAE by 15.4% and 37.5% relative to the next-best model, XGBoost. Paired statistical tests confirmed that this advantage was significant across models. Although the two outputs are strongly correlated, the joint neural network did not outperform the independent ensembles on this moderate-sized dataset, suggesting that strong per-output models are better suited to data of this size. Residual analysis supported these findings, with LightGBM producing residuals randomly dispersed around zero. Overall, the study combines multiple error metrics, statistical testing, and residual diagnostics to guide model selection in correlated multi-output energy prediction. GRAPHICAL ABSTRACT HIGHLIGHTS Compared six independent models and a joint neural network for multi-output building energy prediction. LightGBM gave the lowest error on both heating and cooling loads, confirmed by paired statistical tests. Joint modeling did not outperform independent models on this moderately sized, strongly correlated dataset. The cooling load was consistently harder to predict than the heating load across all models. Feature importance identified relative compactness and glazing variables as the main load drivers.