The Compact Muon Solenoid (CMS) detector is one of two general-purpose detectors on the energy frontier of particle physics at the CERN Large Hadron Collider (LHC). Products of proton-proton collisions at a center of mass energy of 13 TeV are reconstructed in the CMS detector to probe the standard model of particle physics, and to search for processes beyond the standard model. The development of precision algorithms for this reconstruction is therefore a key objective in optimizing the precision of all physics results at CMS. While machine learning techniques are now prevalent at CMS for these tasks, they have largely relied on high-level human-engineered input features. However, much of the disruptive impact of machine learning in industry has been realized by bypassing human feature engineering and instead training deep learning algorithms on low-level data. We have developed a novel machine learning architecture based on dynamic graph neural networks which allows regression directly on low-level detector hits, and we have applied this model to the calibration of electron and photon energies in CMS. In this work, the performance of our new architecture is shown on electrons used in the calibration of the CMS detector, where we obtain an improvement in energy resolution by as much as 10% with respect to the previous state-of-the-art reconstruction method.