Integrating physics-based and data-driven approaches for probabilistic building energy modeling

Building energy modeling is a key tool for optimizing the performance of building energy systems. Historically, a wide spectrum of methods has been explored, ranging from conventional physics-based models to purely data-driven techniques. Recently, hybrid approaches that combine the strengths of both paradigms have gained attention. These include strategies such as learning surrogates for physics-based models, modeling residuals between simulated and observed data, fine-tuning surrogates with real-world measurements, using physics-based outputs as additional inputs for data-driven models, and integrating the physics-based output into the loss function the data-driven model. Despite this progress, two significant research gaps remain. First, most hybrid methods focus on deterministic modeling, often neglecting the inherent uncertainties caused by factors like weather fluctuations and occupant behavior. Second, there has been little systematic comparison within a probabilistic modeling framework. This study addresses these gaps by evaluating five representative hybrid approaches for probabilistic building energy modeling, focusing on quantile predictions of building thermodynamics in a real-world case study. Our results highlight two main findings. First, the performance of hybrid approaches varies across different building room types, but residual learning with a Feedforward Neural Network performs best on average. Notably, the residual approach is the only model that produces physically intuitive predictions when applied to out-of-distribution test data. Second, Quantile Conformal Prediction is an effective procedure for calibrating quantile predictions in case of indoor temperature modeling.