A Model-Agnostic Correction Framework for Short-Term Building Load Forecasting

Shiqiao Zhou; Huanbo Lyu; Holger Schöner; Zipeng Wu; Jessica Deuschel; Freya Wentzel; IAG Wilson; Shuo Wang

cs.IROct 22, 2026

A Model-Agnostic Correction Framework for Short-Term Building Load Forecasting

Authors: Shiqiao Zhou, Huanbo Lyu, Holger Schöner, Zipeng Wu, Jessica Deuschel, Freya Wentzel, IAG Wilson, Shuo Wang

Organizations: School of Computer Science, University of Birmingham, Edgbaston, Birmingham, B15 2TT, West Midlands, United Kingdom · Siemens AG, Munich, 80333, Bavaria, Germany · School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, West Midlands, United Kingdom · Birmingham Energy Institute, University of Birmingham, Edgbaston, Birmingham, B15 2TT, West Midlands, United Kingdom

Abstract

Short-term building load forecasting remains challenging because load patterns can change rapidly with weather and operating conditions. Data-driven forecasting models may become less reliable when the current operating regime is rare or poorly represented during training, even when similar situations exist elsewhere in the historical record. Recent advances in retrieval-augmented time series forecasting offer a promising way to adapt predictions to changing conditions by directly reusing relevant historical cases at inference time. Motivated by this idea, we propose WeL-RAC, a model-agnostic Weather-Load Retrieval-Augmented Correction framework that explicitly retrieves such evidence at prediction time. WeL-RAC retrieves historical cases that are similar to the current condition based on both recent load states and horizon-aligned weather forecasts. Their observed future load trajectories are then aggregated and used to correct the initial prediction, without retraining or modifying the base forecaster. We evaluate WeL-RAC on 31 building cases across three datasets, eight forecasting backbones, and four horizons from 1 to 18 hours. The framework improves the corresponding base forecasters in 90 of 96 dataset-level comparisons. Beyond accuracy, success and failure case studies further illustrate the framework's interpretability by tracing how retrieved historical evidence improves or degrades forecasts. These findings support explicit historical retrieval as an effective and interpretable complement to the building load forecasting.

Figures & tables

Figure 1: Illustration of retrieval-augmented forecasting. Taking building energy forecasting as an example, the process consists of three main steps: (1) the current load, weather, and other information are used to form the forecasting query; (2) similar historical cases are retrieved from a historical data pool based on the current input conditions, and their observed future load trajectories are aggregated as retrieval evidence; and (3) the retrieved evidence is combined with the initial prediction from the forecasting model to produce the final forecast.

Figure 2: Schematic overview of WeL-RAC. The forecasting branch generates an initial prediction from historical load and covariates. The retrieval branch matches the current load state and horizon-aligned weather summary against historical memory banks, retrieves top- $K$ analogue futures, and aggregates their realised trajectories. The correction module performs post-prediction fusion between the initial prediction and the retrieved evidence to produce the final prediction.

Panel of Figure 3 — Figure 3: Conditional weather-summary template for representing both horizon-aligned forecast and historical weather windows. The template fields are defined and selected in Table 1 .

Template field	Source statistic	Phrase selection
horizon	Prediction length $H$	Numeric horizon, expressed in hours for hourly datasets.
time	Start timestamp of the forecast window	night; morning; afternoon; evening.
temp_mean	Mean temperature over the horizon	cold; mild; warm; hot; very hot.
temp_max	Maximum temperature over the horizon	cool; mild; warm; hot; very hot.
temp_min	Minimum temperature over the horizon	cold; cool; mild; warm; hot.
trend	Temperature change	falling quickly; falling; mostly steady; rising; rising quickly.

Table 1: Weather-summary fields and phrase-selection rules.

Dataset	Type	Scope	Building ID	Time span	Resolution	Records per building
AlphaBuilding	Synthetic	9 simulated buildings	1–9	2 years	Hourly	17,520
ASU	Real-world	12 campus buildings	10–21	3 years	Hourly	26,280
UCF	Real-world	10 campus buildings	22–31	3 years	Hourly	26,278

Table 2: Overview of the datasets used in this study.

City	Climate characteristics	Period	Building IDs (efficiency)
Miami	Hot and humid	2002–2003	1 (High) / 2 (Low) / 3 (Standard)
San Francisco	Mild marine	2014–2015	4 (High) / 5 (Low) / 6 (Standard)
Chicago	Cold winters and hot summers	2006–2007	7 (High) / 8 (Low) / 9 (Standard)

Table 3: Composition of the AlphaBuilding dataset.

Model	Hyperparameter	Value range
MLP	learning_rate	$[10^{-4},10^{-2}]$
	batch_size	$\{32,64,128\}$
	train_epochs	$\{10,20,30\}$
	hidden_layers	$\{1,2,3\}$
	hidden_dims_l1 when hidden_layers =1	$\{(16),(24),(32)\}$
	hidden_dims_l2 when hidden_layers =2	$\{(32,16),(48,24),(64,32)\}$

Table 4: Hyperparameter search spaces for the eight forecasting models. Curly braces

\{\cdot\}

denote discrete candidate values, whereas square brackets

[\cdot]

denote continuous search intervals. For continuous learning_rate intervals, sampling is performed on a logarithmic scale; discrete learning_rate values are searched only over the listed candidates.

Component	Hyperparameter	Value range
Retrieval Branch	$\lambda$ ( state weight )	$\{0.20,0.35,0.50,0.65,0.80\}$
	$K$ ( top_K )	$\{10,15,20,30\}$
	$\tau$ ( temperature )	$\{0.10,0.20,0.30\}$
Correction Module	$\alpha$ ( correction coefficient )	$\{0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0\}$

Table 5: Hyperparameter search space for the retrieval branch and correction module.

Method	ASU				AlphaBuilding				UCF				Best
Method	MSE $\downarrow$	MAE $\downarrow$	$R^{2}\uparrow$	MAPE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	$R^{2}\uparrow$	MAPE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	$R^{2}\uparrow$	MAPE $\downarrow$	Best
MLP	543.840	12.382	0.753	0.064	105.593	5.205	0.947	0.093	291.787	9.117	0.789	0.058	1
MLP+Retrieval	532.139	12.237	0.773	0.063	93.421	4.577	0.952	0.080	280.019	9.094	0.793	0.064	11
LightGBM	480.667	11.002	0.784	0.057	129.410	4.413	0.932	0.073	256.371	8.620	0.799	0.073	0
LightGBM+Retrieval	474.789	10.974	0.792	0.057	81.687	4.181	0.957	0.071	250.241	8.544	0.802	0.073	12
DLinear	630.605	13.476	0.777	0.067	540.429	13.798	0.728	0.236	351.967	9.957	0.743	0.063	1

Table 6: Overall forecasting performance. For each building and horizon, all forecasters and their retrieval-enhanced counterparts are evaluated on exactly the same retained forecast origins. Metrics are computed separately for each building–horizon–seed combination and then equally averaged over all buildings, four forecasting horizons (

H\in\{1,6,12,18\}

), and three random seeds (

2021

0

, and

42

) within each dataset. All models use an input length of 24. Lower values are better for MSE, MAE, and MAPE, whereas higher values are better for

R^{2}

. For each backbone, the better result between the original forecaster and its retrieval-enhanced counterpart is highlighted in bold . The Best column reports the number of better results among the 12 dataset–metric comparisons for each forecaster and retrieval pair. All displayed values are rounded to three decimal places; boldface and Best counts are determined using the original unrounded values.

Figure 4: Building-wise relative improvements of the retrieval-enhanced forecasts over the corresponding original forecasters. Results are averaged over the four forecasting horizons (

H\in\{1,6,12,18\}

) and all eight forecasting backbones. Solid bars denote the relative improvement in MSE, while hatched bars denote the relative improvement in MAE. Positive values indicate that retrieval improves the original forecast. Building IDs 1–9, 10–21, and 22–31 correspond to AlphaBuilding, ASU, and UCF, respectively.

Figure 5: Horizon-wise relative improvements of the retrieval-enhanced forecasts over the original forecasters for MSE and MAE. Results are averaged over all buildings within each dataset and over all eight forecasting backbones. In each panel, each forecasting horizon contains two bars: the plain bar denotes the MSE improvement and the hatched bar denotes the MAE improvement. Error bars indicate the interquartile range across forecasting backbones. Positive values indicate that retrieval improves the original forecast.

Method	ASU				AlphaBuilding				UCF				Best
Method	MSE $\downarrow$	MAE $\downarrow$	$R^{2}\uparrow$	MAPE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	$R^{2}\uparrow$	MAPE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	$R^{2}\uparrow$	MAPE $\downarrow$	Best
RAFT	577.894	13.215	0.785	0.068	299.024	10.925	0.850	0.202	317.783	9.794	0.759	0.062	0
SERAF	543.535	12.718	0.798	0.065	249.901	9.864	0.874	0.178	295.230	9.467	0.775	0.061	2
SARAF	546.905	12.857	0.795	0.066	439.627	13.630	0.781	0.254	291.016	9.452	0.782	0.061	0
MLP+Retrieval (load only)	535.118	12.352	0.767	0.064	100.142	4.771	0.949	0.082	288.121	9.202	0.787	0.063	0
MLP+Retrieval (full)	532.139	12.237	0.773	0.063	93.421	4.577	0.952	0.080	280.019	9.094	0.793	0.064	10

Table 7: Comparison with retrieval baselines. Load only denotes retrieval based solely on the proposed load-state summary of WeL-RAC, whereas the full version uses both retrieval branches. For each building and horizon, all methods are evaluated on the same retained forecast origins. Metrics are computed separately for each building–horizon–seed combination and then averaged equally over all buildings, four forecasting horizons (

H\in\{1,6,12,18\}

), and three random seeds within each dataset. All models use an input length of 24. Lower values are better for MSE, MAE, and MAPE, whereas higher values are better for

R^{2}

. The best result among the five rows in each dataset–metric column is highlighted in bold . The Best column counts column-wise wins; both boldface and counts are determined using unrounded values.

Method	ASU				AlphaBuilding				UCF				Best
Method	MSE $\downarrow$	MAE $\downarrow$	$R^{2}\uparrow$	MAPE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	$R^{2}\uparrow$	MAPE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	$R^{2}\uparrow$	MAPE $\downarrow$	Best
Full	539.810	12.440	0.789	0.064	90.619	4.553	0.954	0.079	287.335	9.377	0.777	0.070	7
Forecaster only	592.886	12.903	0.767	0.065	234.025	7.340	0.882	0.125	314.963	9.582	0.762	0.066	1
Retrieval only	674.790	14.834	0.729	0.075	112.735	4.830	0.942	0.081	394.999	11.310	0.681	0.091	0
Load summary only	542.388	12.510	0.787	0.064	96.977	4.732	0.951	0.081	293.568	9.451	0.774	0.069	0
Load raw sequence only	554.645	12.835	0.780	0.065	83.288	4.318	0.958	0.072	325.249	9.941	0.764	0.071	1

Table 8: Dataset-level ablation results averaged over eight forecasting models. For each model, results are first averaged over all buildings, four forecasting horizons (

H\in\{1,6,12,18\}

), and three random seeds; the reported values are then macro-averaged across the eight models. Lower values are better for MSE, MAE, and MAPE, whereas higher values are better for

R^{2}

. Boldface denotes the best result and underlining denotes the second-best result within each column.

Figure 6: Parameter sensitivity on ASU Building 10 using DLinear and PatchTST. Each curve reports the mean MSE over three random seeds for forecasting horizons

H\in\{1,6,12,18\}

, with error bars denoting one standard deviation. Each parameter is varied independently while the remaining configuration is fixed to the values selected by validation. Lower MSE is better.

Memory build time	Memory size	Per-sample latency	Full-test runtime	Test samples
5.668 s	28.775 MiB	6.135 ms	7.232 s	5,238

Table 9: Computational cost of the retrieval-correction mechanism with MLP on UCF Building 30 at forecasting horizon

H=18

Figure 7: Two representative success cases of retrieval-assisted MLP forecasting on ASU Building 10. Both examples use an 18-hour forecasting horizon, a 24-hour input window, and seed 2021. (a) Retrieval corrects an underestimation case with forecast origin 29 May 2019 at 15:00. (b) Retrieval reduces overestimation with forecast origin 17 August 2019 at 17:00. The dark-gray line shows the preceding 24 hourly observations, and the black line with circle markers shows the true future. The blue dashed, green solid, and orange dash-dotted curves denote the MLP prediction, weighted Top-10 retrieval prediction, and final prediction, respectively. Light-gray curves show the input histories and subsequent load trajectories of the

K

retrieved training samples. Historical inputs and continuations are training-period observations, aligned to the query by their respective origins without changing load values.

Figure 8: Two representative failure cases of retrieval-assisted MLP forecasting on UCF Building 30. Both examples use an 18-hour forecasting horizon and seed 2021. (a) A sudden load-drop case with forecast origin 9 August 2019 at 18:00. (b) A persistent low-load case with forecast origin 12 August 2019 at 18:00. The dark-gray line shows the preceding 24 hourly observations, and the black circles indicate the true future. The blue dashed, green solid, and orange dash-dotted curves represent the MLP prediction, weighted Top-10 retrieval prediction, and final prediction, respectively. Light-gray curves show the input histories and subsequent load trajectories of the ten retrieved training samples. Historical samples are aligned by their forecast origins and retain their original load levels.

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

Sarah Al-Shareeda, Gulcihan Ozdemir, Heung Seok Jeon

aComputer System and Technology Department, Faculty of Computer Science and Information Technology, University of Malaya, Malaysia · bInformatics Institute, Istanbul Technical University, Turkey · cComputer Engineering Department Konkuk University South Korea

Quantile Regression Time Series Forecasting Probabilistic Forecasting Electricity Load Forecasting Uncertainty Calibration Probabilistic Time Series Forecasting

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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.

Abstract

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