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

2026-07-14

AI Summary

This study addresses the challenge of inaccurate prediction intervals in smart building load forecasting, often caused by missing inputs and reconstruction errors, which undermines demand response effectiveness. The authors propose a unified day-ahead probabilistic forecasting framework that integrates temporal alignment, missing input reconstruction, and causal feature extraction to systematically compare two uncertainty modeling strategies: modular post-processing quantile regression and in-model quantile learning. Experiments across three medium-scale backbone architectures—RNN, hybrid RNN, and Temporal Fusion Transformer (TFT)—demonstrate that TFT with embedded quantile learning yields more reliable prediction intervals, achieving approximately five times narrower widths and better coverage than modular approaches. Although input reconstruction increases the quantile score by 106%, it leaves interval width largely unchanged, revealing inherent limitations of post-processing methods under reconstruction scenarios.

Abstract

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.

Problem

• probabilistic load forecasting
• input uncertainty
• feature reconstruction
• prediction interval calibration
• smart buildings

Innovation

• probabilistic load forecasting
• input reconstruction uncertainty
• in-model quantile learning
• post-hoc uncertainty
• Temporal Fusion Transformer