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：随着数据采集规模不断扩大，数据驱动建模方法近年来日益流行。经典灰箱模型虽具有物理合理性，但往往存在辨识困难、可扩展性差的问题，且其有限表达能力可能制约模型精度。另一方面，当前依赖神经网络的经典黑箱方法通过从数据中提取统计模式，通常能在大规模应用中取得显著性能。然而，这类方法完全忽视底层物理规律，若基于其决策真实物理系统，可能导致灾难性故障。物理一致性神经网络（PCNNs）近期被提出以解决上述问题，在确保物理一致性的同时，仍借助神经网络实现最先进精度。本研究将PCNNs扩展至建筑温度动态建模，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扩展架构，以此展示该框架的模块化与灵活性，并形式化证明了其物理一致性。案例研究表明，PCNNs在约束结构条件下仍能达到最先进精度，甚至超越经典神经网络模型。研究同时清晰揭示了：完全忽视物理规律的神经网络虽看似表现良好，但实践中可能产生误导。尽管该性能优势伴随计算复杂度的增加，与所有其他物理一致性方法相比，PCNNs仍实现17-35%的精度提升，为发展兼具可扩展性与最先进性能的物理一致性模型开辟了新路径。