Invertible neural networks and more: applications in electronic transport theory

Data-driven and model-driven methods have shown enormous success in both theoretical and applied science. However, when interpreting indirect physical quantities from experimental measurements, the models' validity must be carefully considered. For instance, in electronic structure theory, the values of the effective masses and carrier density are well-defined quantities but are not directly comparable with the measurements. To reconcile the theoretical predictions of a material's effective masses and carrier concentration with experimental analyses, we developed software to automatically link a model band structure to the experimental transport data: electrical conductivity, Seebeck, and Hall coefficients. We first solve very efficiently the direct problem of determining the electronic transport given a multivalley anisotropic parabolic band structure, then we tackle the inverse problem of reconstructing candidates' band structures from the experimental results. The software uses four techniques to tame the inverse problem: reverse Monte Carlo algorithm, invertible neural network, partially observable Markov decision processes, and a Bayesian method.