Haldane Bundles: A Dataset for Learning to Predict the Chern Number of
  Line Bundles on the Torus
Cody Tipton Elizabeth Coda Davis Brown Alyson Bittner Jung Lee Grayson Jorgenson Tegan Emerson Henry Kvinge
Characteristic classes, which are abstract topological invariants associated
with vector bundles, have become an important notion in modern physics with
surprising real-world consequences. As a representative example, the incredible
properties of topological insulators, which are insulators in their bulk but
conductors on their surface, can be completely characterized by a specific
characteristic class associated with their electronic band structure, the first
Chern class. Given their importance to next generation computing and the
computational challenge of calculating them using first-principles approaches,
there is a need to develop machine learning approaches to predict the
characteristic classes associated with a material system. To aid in this
program we introduce the {\emph{Haldane bundle dataset}}, which consists of
synthetically generated complex line bundles on the $2$-torus. We envision this
dataset, which is not as challenging as noisy and sparsely measured real-world
datasets but (as we show) still difficult for off-the-shelf architectures, to
be a testing ground for architectures that incorporate the rich topological and
geometric priors underlying characteristic classes.