# Opening the Black Box: Towards inherently interpretable energy data imputation models using building physics insight

arXiv: https://arxiv.org/abs/2311.16632 · HTML: https://mlsanity.com/paper/2311.16632/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 50 references that are in the map.
- First posted on arXiv 28 Nov 2023.

## Builds on (most cited first, 9 of 9)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [A Fine-Grained Analysis on Distribution Shift](https://mlsanity.com/paper/2110.11328/) (2021)
- [A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications](https://mlsanity.com/paper/2010.02011/) (2020)
- [Physics Informed Neural Networks for Control Oriented Thermal Modeling of Buildings](https://mlsanity.com/paper/2111.12066/) (2021)
- [Designing Inherently Interpretable Machine Learning Models](https://mlsanity.com/paper/2111.01743/) (2021)
- [Physically Consistent Neural Networks for building thermal modeling: theory and analysis](https://mlsanity.com/paper/2112.03212/) (2021)
- [Indoor environment data time-series reconstruction using autoencoder neural networks](https://mlsanity.com/paper/2009.08155/) (2020)
- [Towards Scalable Physically Consistent Neural Networks: an Application to Data-driven Multi-zone Thermal Building Models](https://mlsanity.com/paper/2212.12380/) (2022)
- [EnergyStar++: Towards more accurate and explanatory building energy benchmarking](https://mlsanity.com/paper/1910.14563/) (2019)

## Abstract (arXiv)

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.