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

A charge-preserving method for solving graph neural diffusion networks