One of the major challenges in the development of energy management systems (EMSs) for complex buildings is accurate modeling. To address this, we propose an EMS, which combines a Model Predictive Control (MPC) approach with data-driven model error compensation. The hierarchical MPC approach consists of two layers: An aggregator controls the overall energy flows of the building in an aggregated perspective, while a distributor distributes heating and cooling powers to individual temperature zones. The controllers of both layers employ regression-based error estimation to predict and incorporate the model error. The proposed approach is evaluated in a software-in-the-loop simulation using a physics-based digital twin model. Simulation results show the efficacy and robustness of the proposed approach.