  Combinatorial problems arising in puzzles, origami, and (meta)material design
have rare sets of solutions, which define complex and sharply delineated
boundaries in configuration space. These boundaries are difficult to capture
with conventional statistical and numerical methods. Here we show that
convolutional neural networks can learn to recognize these boundaries for
combinatorial mechanical metamaterials, down to finest detail, despite using
heavily undersampled training sets, and can successfully generalize. This
suggests that the network infers the underlying combinatorial rules from the
sparse training set, opening up new possibilities for complex design of
(meta)materials.
