# Integrating Physics-Based and Data-Driven Approaches for Probabilistic Building Energy Modeling

arXiv: https://arxiv.org/abs/2507.17526 · HTML: https://mlsanity.com/paper/2507.17526/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 53 references that are in the map.
- First posted on arXiv 23 Jul 2025.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Physics Informed Neural Networks for Control Oriented Thermal Modeling of Buildings](https://mlsanity.com/paper/2111.12066/) (2021)
- [Using Bayesian deep learning approaches for uncertainty-aware building energy surrogate models](https://mlsanity.com/paper/2010.03029/) (2020)
- [Probabilistic electric load forecasting through Bayesian Mixture Density Networks](https://mlsanity.com/paper/2012.14389/) (2020)
- [Demand response for residential building heating: Effective Monte Carlo Tree Search control based on physics-informed neural networks](https://mlsanity.com/paper/2312.03365/) (2023)
- [Combining Physics-based and Data-driven Modeling for Building Energy Systems](https://mlsanity.com/paper/2411.01055/) (2024)
- [Physics-informed machine learning for building performance simulation-A review of a nascent field](https://mlsanity.com/paper/2504.00937/) (2025)

## Built on by (most cited first, 1 of 1)

- [In-Context Residual Calibration for Uncertainty Quantification of Energy Time Series over Graphs](https://mlsanity.com/paper/2606.31804/) (2026)

## Abstract (arXiv)

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.