  Quantifying the correlation between the complex structures of amorphous
materials and their physical properties has been a long-standing problem in
materials science. In amorphous Si, a representative covalent amorphous solid,
the presence of a medium-range order (MRO) has been intensively discussed.
However, the specific atomic arrangement corresponding to the MRO and its
relationship with physical properties, such as thermal conductivity, remain
elusive. Here, we solve this problem by combining topological data analysis,
machine learning, and molecular dynamics simulations. By using persistent
homology, we constructed a topological descriptor that can predict the thermal
conductivity. Moreover, from the inverse analysis of the descriptor, we
determined the typical ring features that correlated with both the thermal
conductivity and MRO. The results provide an avenue for controlling the
material characteristics through the topology of nanostructures.
