# Physics-informed linear regression is competitive with two Machine Learning methods in residential building MPC

arXiv: https://arxiv.org/abs/2110.15911 · HTML: https://mlsanity.com/paper/2110.15911/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 80 references that are in the map.
- First posted on arXiv 29 Oct 2021.

## Builds on (most cited first, 15 of 15)

- [Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation](https://mlsanity.com/paper/1609.08144/) (2016)
- [CNN Architectures for Large-Scale Audio Classification](https://mlsanity.com/paper/1609.09430/) (2016)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [Learning Stable Deep Dynamics Models](https://mlsanity.com/paper/2001.06116/) (2020)
- [Optimal Control Via Neural Networks: A Convex Approach](https://mlsanity.com/paper/1805.11835/) (2018)
- [Imposing Hard Constraints on Deep Networks: Promises and Limitations](https://mlsanity.com/paper/1706.02025/) (2017)
- [Data-Enabled Predictive Control: In the Shallows of the DeePC](https://mlsanity.com/paper/1811.05890/) (2018)
- [Physics-constrained Deep Learning of Multi-zone Building Thermal Dynamics](https://mlsanity.com/paper/2011.05987/) (2020)
- [Input Convex Neural Networks for Building MPC](https://mlsanity.com/paper/2011.13227/) (2020)
- [Weakly-Supervised Deep Learning of Heat Transport via Physics Informed Loss](https://mlsanity.com/paper/1807.11374/) (2018)
- [Data-driven Predictive Control for Unlocking Building Energy Flexibility: A Review](https://mlsanity.com/paper/2007.14866/) (2020)
- [Simultaneous identification of linear building dynamic model and disturbance using sparsity-promoting optimization](https://mlsanity.com/paper/1711.06386/) (2017)
- [Distributed Model Predictive Control of Buildings and Energy Hubs](https://mlsanity.com/paper/2110.01734/) (2021)

## Built on by (most cited first, 9 of 9)

- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Physics Informed Neural Networks for Control Oriented Thermal Modeling of Buildings](https://mlsanity.com/paper/2111.12066/) (2021)
- [Physically Consistent Neural Networks for building thermal modeling: theory and analysis](https://mlsanity.com/paper/2112.03212/) (2021)
- [Real-Time Machine-Learning-Based Optimization Using Input Convex Long Short-Term Memory Network](https://mlsanity.com/paper/2311.07202/) (2023)
- [Lessons learned from field demonstrations of model predictive control and reinforcement learning for residential and commercial HVAC: A review](https://mlsanity.com/paper/2503.05022/) (2025)
- [Impact of data for forecasting on performance of model predictive control in buildings with smart energy storage](https://mlsanity.com/paper/2402.12539/) (2024)
- [Partially stochastic deep learning with uncertainty quantification for model predictive heating control](https://mlsanity.com/paper/2504.03350/) (2025)
- [Comparative Field Deployment of Reinforcement Learning and Model Predictive Control for Residential HVAC](https://mlsanity.com/paper/2510.01475/) (2025)
- [Very Exciting: Zero-Shot Model Predictive Control of Buildings via Excitation-Based Generalized Transfer Learning Models](https://mlsanity.com/paper/2609.12853/) (2026)

## Abstract (arXiv)

Because physics-based building models are difficult to obtain as each building is individual, there is an increasing interest in generating models suitable for building MPC directly from measurement data. Machine learning methods have been widely applied to this problem and validated mostly in simulation; there are, however, few studies on a direct comparison of different models or validation in real buildings to be found in the literature. Methods that are indeed validated in application often lead to computationally complex non-convex optimization problems. Here we compare physics-informed Autoregressive-Moving-Average with Exogenous Inputs (ARMAX) models to Machine Learning models based on Random Forests and Input Convex Neural Networks and the resulting convex MPC schemes in experiments on a practical building application with the goal of minimizing energy consumption while maintaining occupant comfort, and in a numerical case study. We demonstrate that Predictive Control in general leads to savings between 26% and 49% of heating and cooling energy, compared to the building's baseline hysteresis controller. Moreover, we show that all model types lead to satisfactory control performance in terms of constraint satisfaction and energy reduction. However, we also see that the physics-informed ARMAX models have a lower computational burden, and a superior sample efficiency compared to the Machine Learning based models. Moreover, even if abundant training data is available, the ARMAX models have a significantly lower prediction error than the Machine Learning models, which indicates that the encoded physics-based prior of the former cannot independently be found by the latter.