  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.
