  Modern scanning probe techniques, like scanning tunneling microscopy (STM),
provide access to a large amount of data encoding the underlying physics of
quantum matter. In this work, we analyze how convolutional neural networks
(CNN) can be employed to learn effective theoretical models from STM data on
correlated moir\'e superlattices. These engineered systems are particularly
well suited for this task as their enhanced lattice constant provides
unprecedented access to intra-unit-cell physics and their tunability allows for
high-dimensional data sets within a single sample. Using electronic nematic
order in twisted double-bilayer graphene (TDBG) as an example, we show that
including correlations between the local density of states (LDOS) at different
energies allows CNNs not only to learn the microscopic nematic order parameter,
but also to distinguish it from heterostrain. These results demonstrate that
neural networks constitute a powerful methodology for investigating the
microscopic details of correlated phenomena in moir\'e systems and beyond.
