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：建筑能耗建模领域的从业者和研究者常面临数据缺失问题。传统上，需要采用深度学习等先进数据驱动方法以反映这类异常的非线性特征。作为与深度学习相关的前沿研究课题，通过在网络中引入先验知识可探索模型在有限数据场景中的适用性。该策略同时能够提升预测结果的可解释性，从而促进方法在工程领域的应用。基于此，本文提出利用物理信息去噪自编码器（Physics-informed Denoising Autoencoders, PI-DAE）对商业建筑进行缺失数据插补。具体而言，所提方法通过向去噪自编码器（Denoising Autoencoder, DAE）的损失函数施加物理启发的软约束。为量化物理组件的贡献，本研究对不同DAE配置进行了消融实验：首先针对室内空气温度、供暖及制冷数据分别优化三个单变量DAE，随后基于前述配置衍生出两个多变量DAE，最终将建筑热平衡方程耦合至最后一个多变量配置形成PI-DAE。此外，采用两类通用基准方法佐证研究结论。结果表明：在多变量去噪自编码器中引入物理知识，可通过优化的物理系数增强模型内在可解释性。尽管所提PI-DAE在重构误差方面未展现显著提升，但其对变化缺失率的鲁棒性增强，以及基于物理系数获得的深刻洞见，为建筑系统及建成环境中的更广泛应用创造了机遇。