Towards scalable physically consistent neural networks: An application to data-driven multi-zone thermal building models

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, and applied to zone temperature modeling. In this work, we scale PCNNs to model the temperature dynamics of buildings with several connected thermal zones and propose a thorough comparison with classical gray-box and black-box methods. More precisely, we design three distinct PCNN extensions with different levels of information sharing between the modeled zones, 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. [Display omitted] •Gray-box building models do not scale well and have a limited expressiveness.•Classical black-box methods attain great performance but remain physics-agnostic.•Multi-zone Physically Consistent Neural Networks (PCNNs) are proposed.•PCNNs respect given physical rules by design despite relying on Neural Networks.•They simultaneously achieve state-of-the-art accuracy on a building case study.