  Nanoporous materials are a promising platform for thermoelectrics in that
they offer high thermal conductivity tunability while preserving good
electrical properties, a crucial requirement for high- effciency thermal energy
conversion. Understanding the impact of the pore arrangement on thermal
transport is pivotal to engineering realistic materials, where pore disorder is
unavoidable. Although there has been considerable progress in modeling thermal
size effects in nanostructures, it has remained a challenge to screen such
materials over a large phase space due to the slow simulation time required for
accurate results. We use density functional theory in connection with the
Boltzmann transport equation, to perform calculations of thermal conductivity
in disordered porous materials. By leveraging graph theory and regressive
analysis, we identify the set of pores representing the phonon bottleneck and
obtain a descriptor for thermal transport, based on the sum of the pore-pore
distances between such pores. This approach provides a simple tool to estimate
phonon suppression in realistic porous materials for thermoelectric
applications and enhance our understanding of heat transport in disordered
materials.
