  Topological concepts open many new horizons for photonic devices, from
integrated optics to lasers. The complexity of large scale topological devices
asks for an effective solution of the inverse problem: how best to engineer the
topology for a specific application? We introduce a novel machine learning
approach to the topological inverse problem. We train a neural network system
with the band structure of the Aubry-Andre-Harper model and then adopt the
network for solving the inverse problem. Our application is able to identify
the parameters of a complex topological insulator in order to obtain protected
edge states at target frequencies. One challenging aspect is handling the
multivalued branches of the direct problem and discarding unphysical solutions.
We overcome this problem by adopting a self-consistent method to only select
physically relevant solutions. We demonstrate our technique in a realistic
topological laser design and by resorting to the widely available open-source
TensorFlow library. Our results are general and scalable to thousands of
topological components. This new inverse design technique based on machine
learning potentially extends the applications of topological photonics, for
example, to frequency combs, quantum sources, neuromorphic computing and
metrology.
