Learning-based Probabilistic Load Forecasting with Post-hoc and In-model Uncertainty

Research Question and Approach

This paper investigates how to best quantify uncertainty in smart-building load forecasting when the model is trained on high-resolution, multivariate data but must operate on sparse, feature-limited data at inference. Because deployment often lacks key sensors, missing features must be reconstructed, which introduces errors that can propagate through the model. The authors compare two primary strategies for uncertainty quantification: a modular post-hoc approach (where uncertainty is added after a point forecast is made) and an integrated in-model approach (where quantile learning is embedded directly into the training process).

The researchers evaluate these strategies using three deep learning backbones—BiLSTM, BiGRU-LSTM, and the Temporal Fusion Transformer (TFT)—within a unified framework. The study uses a controlled experimental setup where data splits, preprocessing, and training budgets are held constant to isolate the impact of the uncertainty placement method on forecast accuracy and interval calibration.

The study reveals that the effectiveness of uncertainty placement is highly dependent on the model architecture. Integrated quantile learning proved most reliable when paired with the TFT, achieving superior Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) while producing prediction intervals approximately five times narrower than those generated by the modular post-hoc scheme at nominal coverage levels.

A critical finding is that the model does not automatically absorb the uncertainty introduced by input reconstruction. Reconstruction-sensitivity tests showed that while reconstructed inputs significantly increased the Quantile Score (a measure of probabilistic forecast quality), the interval widths remained largely unchanged. This suggests that post-hoc residual methods are fundamentally limited in their ability to handle the specific noise patterns generated by feature reconstruction, as they lack visibility into the model's internal state during the inference process.