  Many scientific problems seek to find the ground state in a rugged energy
landscape, a task that becomes prohibitively difficult for large systems.
Within a particular class of problems, however, the short-range correlations
within energy minima might be independent of system size. Can these
correlations be inferred from small problems with known ground states to
accelerate the search for the ground states of larger problems? Here, we
demonstrate the strategy on Ising spin glasses, where the interaction matrices
are drawn from protein contact maps. We use graph neural network to learn the
mapping from an interaction matrix $J$ to a ground state configuration,
yielding guesses for the set of most probable configurations. Given these
guesses, we show that ground state configurations can be searched much faster
than in vanilla simulated annealing. For large problems, a model trained on
small $J$ matrices predicts a configurations whose energy is much lower than
those obtained by simulated annealing, indicating the size generalizability of
the strategy.
