Silica glass is an essential material employed in applications such as window glass, optical fibers, and semiconductor manufacturing owing to its high transparency and chemical stability. Although glass is generally considered to exhibit a disordered atomic arrangement, X-ray and neutron diffraction experiments on silica glass have revealed sharp peaks. This suggests the presence of medium-range ordered (MRO) atomic arrangements in glass. The MRO structures are related to the transparency and other properties of silica glass. Thus, information on these structures must be revealed to facilitate the development of functional glass materials. Owing to the difficulty in experimentally determining the atomic arrangement of glass, high-precision simulations are required for structural analysis for uncovering ordered structures in glass. This study conducted the structural analysis of silica glass using the "machine learning molecular dynamics method," which facilitates high-speed and accurate calculations via the training of a machine learning model with quantum mechanical calculations. We successfully replicated the diffraction peaks of silica glass by leveraging the "machine learning molecular dynamics method," which enables fast and highly accurate calculations by training machine learning models with quantum mechanical computation results. Furthermore, to elucidate the MRO atomic arrangements within glass, it is crucial to uncover the atomic connections and their geometric structures. By employing mathematical techniques such as persistent homology, we characterized the details of MRO structures hidden within the disordered glass matrix.
 These simulation and mathematical methods are expected to accelerate the development of functional glass materials through the elucidation and analysis of the three-dimensional atomic arrangements in glass, which are difficult to determine through experiments alone.

Part of this study was conducted using mdx: a platform for building data-empowered society (Project ID: jh230069), and supported by JSPS KAKENHI Grant-in-Aid for Scientific Research (C) (Grant Number JP23K04637), "Machine-Learning Molecular Dynamics for Nuclear Fuel Materials."