Missing data are frequently observed by practitioners and researchers in the building energy modeling community. In this regard, advanced data-driven solutions, such as Deep Learning methods, are typically required to reflect the non-linear behavior of these anomalies. As an ongoing research question related to Deep Learning, a model's applicability to limited data settings can be explored by introducing prior knowledge in the network. This same strategy can also lead to more interpretable predictions, hence facilitating the field application of the approach. For that purpose, the aim of this paper is to propose the use of Physics-informed Denoising Autoencoders (PI-DAE) for missing data imputation in commercial buildings. In particular, the presented method enforces physics-inspired soft constraints to the loss function of a Denoising Autoencoder (DAE). In order to quantify the benefits of the physical component, an ablation study between different DAE configurations is conducted. First, three univariate DAEs are optimized separately on indoor air temperature, heating, and cooling data. Then, two multivariate DAEs are derived from the previous configurations. Eventually, a building thermal balance equation is coupled to the last multivariate configuration to obtain PI-DAE. Additionally, two commonly used benchmarks are employed to support the findings. It is shown how introducing physical knowledge in a multivariate Denoising Autoencoder can enhance the inherent model interpretability through the optimized physics-based coefficients. While no significant improvement is observed in terms of reconstruction error with the proposed PI-DAE, its enhanced robustness to varying rates of missing data and the valuable insights derived from the physics-based coefficients create opportunities for wider applications within building systems and the built environment.

翻译：建筑能源建模领域的实践者和研究人员经常观测到数据缺失现象。针对此类问题，通常需要采用深度学习等先进的数据驱动方法，以反映这些异常现象的非线性行为。作为深度学习相关的一个持续研究课题，通过在网络中引入先验知识，可以探索模型在有限数据场景下的适用性。同一策略还能提升预测结果的可解释性，从而促进该方法在工程领域的应用。为此，本文旨在提出使用物理信息约束去噪自编码器（Physics-informed Denoising Autoencoders, PI-DAE）对商业建筑进行缺失数据填补。具体而言，所提出的方法在去噪自编码器（Denoising Autoencoder, DAE）的损失函数中施加了基于物理启发的软约束。为量化物理组件的贡献，对不同DAE配置进行了消融研究。首先，分别针对室内空气温度、供暖及制冷数据对三种单变量DAE进行独立优化；然后，基于前述配置衍生出两种多变量DAE；最后，将建筑热平衡方程与最终的多变量配置相结合，得到PI-DAE。此外，采用两种通用基准方法辅助验证结论。研究表明：在多变量去噪自编码器中引入物理知识，可通过优化的物理参数提升模型固有能力的内生可解释性。虽然所提出的PI-DAE在重构误差方面未见显著提升，但其在应对不同缺失率数据时表现出的更强鲁棒性，以及从物理参数中获得的宝贵洞察，为建筑系统及建成环境领域的更广泛应用创造了机遇。