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

Smart-building load forecasters are often trained offline on dense, multivariate, high-frequency data, but deployment may provide only hourly, feature-limited inputs.

Missing features must then be reconstructed, and their errors can propagate through the model.

If this input uncertainty is not reflected, prediction intervals may become miscalibrated, affecting demand-response scheduling.

Our work examines where uncertainty should be placed once inference inputs are reconstructed.

We develop a unified one-day-ahead probabilistic forecasting framework that aligns temporal resolution, reconstructs the unavailable inputs, and derives causal features, and we compare a modular post-hoc residual-quantile scheme with an integrated in-model quantile-learning scheme.

The comparison uses three mid-scale Deep Learning (DL) backbones: recurrent, hybrid recurrent, and attention-based Temporal Fusion Transformer (TFT) models, under identical inputs, forecasting horizon, preprocessing rules, and training budgets.

Results show that uncertainty placement is backbone-dependent.

Integrated quantile learning is most reliable with the TFT, yielding 2.2-3.6% MAPE and 28-83W RMSE on the labeled test window, while producing intervals about 5x narrower than the modular intervals at the closest-to-nominal coverage level.

Diebold-Mariano tests support the TFT ranking and the mixed behavior of the recurrent backbones.

A reconstruction-sensitivity test shows that reconstructed inputs increase the Quantile Score (QS) by 106% while interval width remains nearly unchanged, indicating that the model does not automatically absorb reconstruction-induced uncertainty.

Robustness checks against non-DL baselines and seasonal hold-out weeks support this ranking.

Our results expose the limits of post-hoc residual quantiles when inference depends on reconstructed inputs.