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：随着数据采集日益增多，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，但通常难以辨识和扩展，其精度可能受限于有限的表达能力。另一方面，经典黑箱方法（当今通常依赖神经网络）通过从数据中提取统计模式，即便在大规模应用中也能取得令人瞩目的性能。然而，这类方法完全忽视潜在物理定律，若基于其决策真实物理系统，可能导致潜在灾难性故障。物理一致性神经网络（Physically Consistent Neural Networks, PCNNs）近期被开发以解决上述问题，在保证物理一致性的同时利用神经网络实现顶尖精度。本研究将PCNN扩展应用于建筑温度动态建模，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，由此展现该架构的模块化与灵活性，并形式化证明了其物理一致性。在所述案例研究中，PCNN展现出顶尖精度，尽管结构受限，其性能甚至超越经典神经网络模型。我们的研究还清晰揭示了神经网络在完全忽略物理规律时可能表现出看似良好的性能——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PCNN相比其他所有物理一致性方法实现了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性模型开辟了道路。