  Because physics-based building models are difficult to obtain as each
building is individual, there is an increasing interest in generating models
suitable for building MPC directly from measurement data. Machine learning
methods have been widely applied to this problem and validated mostly in
simulation; there are, however, few studies on a direct comparison of different
models or validation in real buildings to be found in the literature. Methods
that are indeed validated in application often lead to computationally complex
non-convex optimization problems. Here we compare physics-informed
Autoregressive-Moving-Average with Exogenous Inputs (ARMAX) models to Machine
Learning models based on Random Forests and Input Convex Neural Networks and
the resulting convex MPC schemes in experiments on a practical building
application with the goal of minimizing energy consumption while maintaining
occupant comfort, and in a numerical case study. We demonstrate that Predictive
Control in general leads to savings between 26% and 49% of heating and cooling
energy, compared to the building's baseline hysteresis controller. Moreover, we
show that all model types lead to satisfactory control performance in terms of
constraint satisfaction and energy reduction. However, we also see that the
physics-informed ARMAX models have a lower computational burden, and a superior
sample efficiency compared to the Machine Learning based models. Moreover, even
if abundant training data is available, the ARMAX models have a significantly
lower prediction error than the Machine Learning models, which indicates that
the encoded physics-based prior of the former cannot independently be found by
the latter.
