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

arXiv: https://arxiv.org/abs/2504.03350 · HTML: https://mlsanity.com/paper/2504.03350/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 56 references that are in the map.
- First posted on arXiv 4 Apr 2025.

## Builds on (most cited first, 14 of 14)

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- [Do Bayesian Neural Networks Need To Be Fully Stochastic?](https://mlsanity.com/paper/2211.06291/) (2022)
- [GradDiv: Adversarial Robustness of Randomized Neural Networks via Gradient Diversity Regularization](https://mlsanity.com/paper/2107.02425/) (2021)
- [Physics-constrained Deep Learning of Multi-zone Building Thermal Dynamics](https://mlsanity.com/paper/2011.05987/) (2020)
- [Physics Informed Neural Networks for Control Oriented Thermal Modeling of Buildings](https://mlsanity.com/paper/2111.12066/) (2021)
- [Frequentist Uncertainty in Recurrent Neural Networks via Blockwise Influence Functions](https://mlsanity.com/paper/2006.13707/) (2020)
- [Physically Consistent Neural Networks for building thermal modeling: theory and analysis](https://mlsanity.com/paper/2112.03212/) (2021)
- [Physics-informed linear regression is competitive with two Machine Learning methods in residential building MPC](https://mlsanity.com/paper/2110.15911/) (2021)
- [BayesPy: Variational Bayesian Inference in Python](https://mlsanity.com/paper/1410.0870/) (2014)
- [Towards Scalable Physically Consistent Neural Networks: an Application to Data-driven Multi-zone Thermal Building Models](https://mlsanity.com/paper/2212.12380/) (2022)
- [Demand response for residential building heating: Effective Monte Carlo Tree Search control based on physics-informed neural networks](https://mlsanity.com/paper/2312.03365/) (2023)

## Abstract (arXiv)

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.