  The aim of this paper is to give a systematic mathematical interpretation of
the diffusion problem on which Graph Neural Networks (GNNs) models are based.
The starting point of our approach is a dissipative functional leading to
dynamical equations which allows us to study the symmetries of the model. We
discuss the conserved charges and provide a charge-preserving numerical method
for solving the dynamical equations. In any dynamical system and also in GRAph
Neural Diffusion (GRAND), knowing the charge values and their conservation
along the evolution flow could provide a way to understand how GNNs and other
networks work with their learning capabilities.
