  Computational electromagnetics (CEM) is employed to numerically solve
Maxwell's equations, and it has very important and practical applications
across a broad range of disciplines, including biomedical engineering,
nanophotonics, wireless communications, and electrodynamics. The main
limitation of existing CEM methods is that they are computationally demanding.
Our work introduces a leap forward in scientific computing and CEM by proposing
an original solution of Maxwell's equations that is grounded on graph neural
networks (GNNs) and enables the high-performance numerical resolution of these
fundamental mathematical expressions. Specifically, we demonstrate that the
update equations derived by discretizing Maxwell's partial differential
equations can be innately expressed as a two-layer GNN with static and
pre-determined edge weights. Given this intuition, a straightforward way to
numerically solve Maxwell's equations entails simple message passing between
such a GNN's nodes, yielding a significant computational time gain, while
preserving the same accuracy as conventional transient CEM methods. Ultimately,
our work supports the efficient and precise emulation of electromagnetic wave
propagation with GNNs, and more importantly, we anticipate that applying a
similar treatment to systems of partial differential equations arising in other
scientific disciplines, e.g., computational fluid dynamics, can benefit
computational sciences
