Chemical and Physical Property Prediction of Materials from the Geometry and Topology of Scalar Fields

Many material properties are encoded in the shapes of their underlying structures: bonds can be quantitatively analyzed from the geometry of electron densities, and mass transport can be simulated from the shapes of energy potentials. We present an algorithm for the geometric and topological analysis of general scalar fields and demonstrate how it can be used to study material stability, mass transport (e.g. ions in solid-state electrolytes or gases in metal–organic frameworks), and the generation of machine-learning-ready geometric descriptors.