  Magnetic moments near zigzag edges in graphene allow complex nanostructures
with customised spin properties to be realised. However, computational costs
restrict theoretical investigations to small or perfectly periodic structures.
Here we demonstrate that a machine-learning approach, using only geometric
input, can accurately estimate magnetic moment profiles, allowing arbitrarily
large and disordered systems to be quickly simulated. Excellent agreement is
found with mean-field Hubbard calculations, and important electronic, magnetic
and transport properties are reproduced using the estimated profiles. This
approach allows the magnetic moments of experimental-scale systems to be
quickly and accurately predicted, and will speed-up the identification of
promising geometries for spintronic applications. While machine-learning
approaches to many-body interactions have largely been limited to exact
solutions of complex models at very small scales, this work establishes that
they can be successfully applied at very large scales at mean-field levels of
accuracy.
