Inverse Physics-Informed Neural Networks for thermal parameter estimation of existing buildings

Building energy modeling is crucial for understanding the thermal behavior of buildings, but traditional physics-based models struggle with uncertainties such as occupant behavior and require extensive data collection. Data-driven models, while faster and more accurate, lack generalization and interpretability of physical laws like thermodynamics.

The Resistance-Capacitance (RC) model simplifies building components into resistances and capacities, providing a balance of simplicity, interpretability, and efficiency. By integrating RC models with data-driven approaches, including Neural Networks (NN), as seen in Physics-Informed Neural Networks (PINNs), it’s possible to extract thermal properties from sparse data and improve modeling accuracy. Recent studies show that PINNs can enhance indoor temperature prediction accuracy by up to 40% compared to traditional RC models, making them valuable for building retrofitting, control-oriented applications, and energy efficiency analysis.

This paper applies the PINN model, which uses the RC model as its base physics equation, for inverse energy modeling of existing single-family homes. We utilize a smart thermostat dataset from 234 Illinois houses, obtained through ecobee Donate Your Data program, focusing on the heating season from December 2021 to February 2022.

The PINN model combines a 2R2C physical model with a NN to approximate indoor temperature. The NN maps input features like outdoor temperature and solar radiation to the output, indoor temperature, while the 2R2C model represents the building’s thermal dynamics using two resistances and two capacitances. The model’s loss function includes the mean squared error (MSE) between predicted and actual temperatures (NN loss) and residuals from the 2R2C differential equations (physical loss). The model is trained with the Adam optimizer to adjust NN weights and 2R2C parameters, ultimately identifying optimal thermal properties for each building.

The model’s performance was evaluated using a sample house dataset from Illinois during the winter period. The model’s MSE was calculated to be 0.81, which is considered acceptable. Additionally, the optimized thermal properties including R and C values fell within an acceptable range, confirming the model’s robustness and generalizability.

However, the model struggled to predict short-term fluctuations in indoor temperatures. To address this, we plan to implement a Recurrent Neural Network, which excels at predicting time-series patterns. The enhanced model will be tested on data from over 200 houses. The proposed model will be compared with classical RC and NN models in terms of accuracy, speed, and robustness.