  Topological materials present unconventional electronic properties that make
them attractive for both basic science and next-generation technological
applications. The majority of currently known topological materials have been
discovered using methods that involve symmetry-based analysis of the quantum
wavefunction. Here we use machine learning to develop a simple-to-use heuristic
chemical rule that diagnoses with a high accuracy whether a material is
topological using only its chemical formula. This heuristic rule is based on a
notion that we term topogivity, a machine-learned numerical value for each
element that loosely captures its tendency to form topological materials. We
next implement a high-throughput procedure for discovering topological
materials based on the heuristic topogivity-rule prediction followed by ab
initio validation. This way, we discover new topological materials that are not
diagnosable using symmetry indicators, including several that may be promising
for experimental observation.
