Physics-Guided Neural ODEs for Building Thermal Prediction and Model Predictive Control

Abstract

Building supervisory control requires accurate, prior-consistent, and computationally tractable thermal models. This study proposes a physics-guided neural ordinary differential equation (PG-NODE) framework for thermal prediction and model predictive control (MPC). It combines a resistance–capacitance (RC)-inspired reference, a neural residual, RC-prior directional regularization, and validation-based checkpoint selection; the selected predictor remains fixed during MPC operation. Using 30 min EnergyPlus data from five zones, the framework was evaluated through held-out prediction, Gaussian noise and control-input-mismatch tests, ablation, and surrogate-based closed-loop experiments. Long short-term memory achieved the lowest prediction root mean square error (RMSE), whereas PG-NODE achieved the lowest RMSE among the evaluated neural ODE models and the lowest directional inconsistency rate among learned nonlinear models. In five-seed × five-window BACK SPACE experiments using independently trained, fixed PG-NODE surrogate environments rather than direct EnergyPlus interaction, fixed-block analysis supported lower reference-tracking RMSE for PG-NODE-MPC than for rule-based control and lower tariff-weighted normalized control effort than for the extended Kalman filter-based RC-MPC benchmark. This benchmark achieved the lowest descriptive mean reference-tracking RMSE and total objective. Mean PG-NODE-MPC optimization time was 0.86 s. Results suggest the potential for low-frequency building management system supervisory decision support, subject to physical command mapping and staged field validation.