# Physics-constrained Deep Learning of Multi-zone Building Thermal Dynamics

arXiv: https://arxiv.org/abs/2011.05987 · HTML: https://mlsanity.com/paper/2011.05987/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2020.

## Built on by (most cited first, 30 of 32)

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- [A Distributed ADMM-based Deep Learning Approach for Thermal Control in Multi-Zone Buildings under Demand Response Events](https://mlsanity.com/paper/2312.05073/) (2023)
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## Abstract (arXiv)

We present a physics-constrained control-oriented deep learning method for modeling building thermal dynamics. The proposed method is based on the systematic encoding of physics-based prior knowledge into a structured recurrent neural architecture. Specifically, our method incorporates structural priors from traditional physics-based building modeling into the neural network thermal dynamics model structure. Further, we leverage penalty methods to provide inequality constraints, thereby bounding predictions within physically realistic and safe operating ranges. Observing that stable eigenvalues accurately characterize the dissipativeness of the system, we additionally use a constrained matrix parameterization based on the Perron-Frobenius theorem to bound the dominant eigenvalues of the building thermal model parameter matrices. We demonstrate the proposed data-driven modeling approach's effectiveness and physical interpretability on a dataset obtained from a real-world office building with 20 thermal zones. Using only 10 days' measurements for training, we demonstrate generalization over 20 consecutive days, significantly improving the accuracy compared to prior state-of-the-art results reported in the literature.