Partially stochastic deep learning with uncertainty quantification for model predictive heating control

TL;DR

The work addresses energy efficiency in building heating by improving indoor temperature prediction for model predictive control (MPC) with uncertainty quantification. It introduces a partially stochastic deep learning model, LSTM+BNN, which places a probabilistic prior on the first linear layer while keeping the remainder deterministic, and trains via variational inference to produce predictive uncertainty. On a large real-world dataset of 100 buildings, the LSTM+BNN outperforms an industry-proven reference model by more than 40% RMSE for the $H=48$ hour horizon and provides a calibrated uncertainty distribution, enabling pre-assessment of model competency for MPC decisions. The approach balances predictive accuracy with transparency and scalability, supporting uncertainty-aware integration into industrial heating MPC and offering a pathway toward more reliable, energy-efficient thermal management in buildings.

Abstract

Making the control of building heating systems more energy efficient is crucial for reducing global energy consumption and greenhouse gas emissions. Traditional rule-based control methods use a static, outdoor temperature-dependent heating curve to regulate heat input. This open-loop approach fails to account for both the current state of the system (indoor temperature) and free heat gains, such as solar radiation, often resulting in poor thermal comfort and overheating. Model Predictive Control (MPC) addresses these drawbacks by using predictive modeling to optimize heating based on a building's learned thermal behavior, current system state, and weather forecasts. However, current industrial MPC solutions often employ simplified physics-inspired indoor temperature models, sacrificing accuracy for robustness and interpretability. While purely data-driven models offer superior predictive performance and therefore more accurate control, they face challenges such as a lack of transparency. To bridge this gap, we propose a partially stochastic deep learning (DL) architecture, dubbed LSTM+BNN, for building-specific indoor temperature modeling. Unlike most studies that evaluate model performance through simulations or limited test buildings, our experiments across a comprehensive dataset of 100 real-world buildings, under various weather conditions, demonstrate that LSTM+BNN outperforms an industry-proven reference model, reducing the average prediction error measured as RMSE by more than 40% for the 48-hour prediction horizon of interest. Unlike deterministic DL approaches, LSTM+BNN offers a critical advantage by enabling pre-assessment of model competency for control optimization through uncertainty quantification. Thus, the proposed model shows significant potential to improve thermal comfort and energy efficiency achieved with heating MPC solutions.

Figures (8)

• Figure 1: Conservation of thermal energy in a building. Here $\Delta Q_{\text{stored}} = \frac{\text{d}Q_{\text{stored}}}{\text{d}t}$ describes the rate of change of the thermal energy stored by the indoor air mass over time $t$.
• Figure 2: Illustration of an LSTM layer with $L$ LSTM units connected to an MLP with two linear layers. The weights and biases in the LSTM are represented in stacked form as the vector $\boldsymbol{z}_1$. Similarly, the weights and biases of the MLP layers are grouped into $\boldsymbol{z}_2$ and $\boldsymbol{z}_3$, respectively.
• Figure 3: Performance of the LSTM+BNN with different prior variances $\beta^2$ as RMSE \ref{['RMSE']} for different prediction horizon lengths $K\in[1, 6, 48]$. Orange lines are the RMSE distribution medians, while boxes and whiskers indicate the central $50\%$ and $95\%$ of the data, respectively. Note the different scales on the Y-axes.
• Figure 4: a) and b): 48-hour indoor temperature predictions for two different test samples. c) and d): Predictive uncertainties of the LSTM+BNN corresponding to the test samples shown in a) and b), respectively. Uncertainty is quantified as the cumulative standard deviation across each prediction's $N_S=10$ posterior predictive samples.
• Figure 5: Performance of the three models as RMSE \ref{['RMSE']} distributions into different prediction horizon lengths $K\in[1, 6, 48]$. Orange lines are the RMSE distribution medians, while boxes and whiskers indicate the central $50\%$ and $95\%$ of the data, respectively. Note the different scales on the Y-axes.