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The design of periodic nanostructures allows to tailor the transport ofphotons, phonons, and matter waves for specific applications. Recent years haveseen a further expansion of this field by engineering topological properties.However, what is missing currently are efficient ways to rapidly explore andoptimize band structures and to classify their topological characteristics, forarbitrary unit cell geometries. In this work, we show how deep learning canaddress this challenge. We introduce an approach where a neural network firstmaps the geometry to a tight-binding model. This allows us to exploit anyunderlying space group and predict the symmetries of Bloch waves. Wedemonstrate how that helps to rapidly categorize a large set of geometries interms of their band representations, identifying designs for fragiletopologies. Engineering of domain walls and optimization are also acceleratedby orders of magnitude. The approach is general enough to permit futureapplications to the geometry discovery in other classes of materials (e.g.active and nonlinear metamaterials).

Rapid Exploration of Topological Band Structures using Deep Learning