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.

翻译：随着越来越多数据的采集，数据驱动建模方法近年来日益流行。经典灰箱模型虽物理基础坚实，但辨识与扩展过程繁琐，且其表达能力受限可能影响精度。而现代经典黑箱方法通常依赖神经网络，通过从数据中提取统计模式，即便在大规模场景下也能实现卓越性能。然而，此类方法完全无视潜在物理定律，若基于其决策指导现实物理系统，可能导致灾难性后果。物理一致神经网络（PCNNs）近期被提出以解决上述问题，它在确保物理一致性的同时，仍借助神经网络达到顶尖精度。本研究将PCNNs扩展至建筑温度动力学建模，并与经典灰箱及黑箱方法进行系统比较。具体而言，我们设计了三种不同的PCNN衍生结构，以此展示该架构的模块化与灵活性，并严格证明其物理一致性。在所述案例研究中，PCNNs展现了顶尖精度，即便其结构受约束，性能仍超越经典基于神经网络的模型。我们的研究更清晰揭示了神经网络在完全忽视物理背景时可能呈现表面优异的性能，这在实际应用中具有误导性。尽管该性能以计算复杂度为代价，但PCNNs相比其他所有物理一致方法仍实现了17-35%的精度提升，为构建兼具可扩展性与顶尖性能的物理一致模型开辟了道路。