# Towards Scalable Physically Consistent Neural Networks: an Application to Data-driven Multi-zone Thermal Building Models

arXiv: https://arxiv.org/abs/2212.12380 · HTML: https://mlsanity.com/paper/2212.12380/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 66 references that are in the map.
- First posted on arXiv 23 Dec 2022.

## Builds on (most cited first, 20 of 20)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Confounding variables can degrade generalization performance of radiological deep learning models](https://mlsanity.com/paper/1807.00431/) (2018)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Visualizing and Understanding Recurrent Networks](https://mlsanity.com/paper/1506.02078/) (2015)
- [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017)
- [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)
- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [Linearly Constrained Neural Networks](https://mlsanity.com/paper/2002.01600/) (2020)
- [Physically Consistent Neural Networks for building thermal modeling: theory and analysis](https://mlsanity.com/paper/2112.03212/) (2021)
- [Data-driven control of room temperature and bidirectional EV charging using deep reinforcement learning: simulations and experiments](https://mlsanity.com/paper/2103.01886/) (2021)
- [Near-optimal Deep Reinforcement Learning Policies from Data for Zone Temperature Control](https://mlsanity.com/paper/2203.05434/) (2022)
- [Generating captions without looking beyond objects](https://mlsanity.com/paper/1610.03708/) (2016)
- [Physically Consistent Neural ODEs for Learning Multi-Physics Systems](https://mlsanity.com/paper/2211.06130/) (2022)

## Built on by (most cited first, 4 of 4)

- [Combining Physics-based and Data-driven Modeling for Building Energy Systems](https://mlsanity.com/paper/2411.01055/) (2024)
- [Data-driven adaptive building thermal controller tuning with constraints: A primal-dual contextual Bayesian optimization approach](https://mlsanity.com/paper/2310.00758/) (2023)
- [Opening the Black Box: Towards inherently interpretable energy data imputation models using building physics insight](https://mlsanity.com/paper/2311.16632/) (2023)
- [Partially stochastic deep learning with uncertainty quantification for model predictive heating control](https://mlsanity.com/paper/2504.03350/) (2025)

## Abstract (arXiv)

With more and more data being collected, data-driven modeling methods have been gaining in popularity in recent years. While physically sound, classical gray-box models are often cumbersome to identify and scale, and their accuracy might be hindered by their limited expressiveness. On the other hand, classical black-box methods, typically relying on Neural Networks (NNs) nowadays, often achieve impressive performance, even at scale, by deriving statistical patterns from data. However, they remain completely oblivious to the underlying physical laws, which may lead to potentially catastrophic failures if decisions for real-world physical systems are based on them. Physically Consistent Neural Networks (PCNNs) were recently developed to address these aforementioned issues, ensuring physical consistency while still leveraging NNs to attain state-of-the-art accuracy. In this work, we scale PCNNs to model building temperature dynamics and propose a thorough comparison with classical gray-box and black-box methods. More precisely, we design three distinct PCNN extensions, thereby exemplifying the modularity and flexibility of the architecture, and formally prove their physical consistency. In the presented case study, PCNNs are shown to achieve state-of-the-art accuracy, even outperforming classical NN-based models despite their constrained structure. Our investigations furthermore provide a clear illustration of NNs achieving seemingly good performance while remaining completely physics-agnostic, which can be misleading in practice. While this performance comes at the cost of computational complexity, PCNNs on the other hand show accuracy improvements of 17-35% compared to all other physically consistent methods, paving the way for scalable physically consistent models with state-of-the-art performance.