Machine-Learning Approach to the Extraction of Microscopic Information from Experimental Data

While theories such as statistical mechanics and solid-state physics enable the computation of macroscopic quantities using the microscopic Hamiltonian, modelling of the Hamiltonian frequently yields results with poor performance. Toward solving this issue, we propose a machine-learning approach to extract microscopic information from experimental data. Our approach is based on the manifold-learning approach which is an unsupervised machine-learning approach. As one of the applications of our approach, molecular information on liquids is extracted from the data on the thermal properties of 98 liquid substances [1]. It is found that information related to the intermolecular forces, molecular weight, and the number of carbons is successfully extracted. We also applied our approach to three-dimensional electron density maps obtained using the simulation for X-ray ptychography of fuel cells. It is found that the information related to porous structures of fuel cells is successfully extracted. Also, the relation between the maps and the diffusion coefficients can be established using the information. These results indicate the success of the extraction of molecular information using our approach.

[1] S. Arai, G. Kikugawa, and T. Yoshidome, J. Mol. Liq. 414 (2024), 126251.