Machine learning for locally periodic structure transmission modelling

This research aims to obtain an analytical transmission model for locally periodic structures with the approach of data-driven physics. So far, this task has been done mainly numerically for non-trivial geometries. From a dataset of Bloch phases generated for given frequency band and structure geometry parameters, it is possible to learn equations relating dispersion relation to axis-symmetric geometry. The dataset is transformed into a lower-dimensional space by applying Principal Component Analysis (PCA) to reduce the complexity of the problem. In the newly obtained coordinate system, the lower-dimensional patterns are extracted via symbolic regression. The resulting model is interpretable in terms of underlying physics and can be used, e.g., to propose an optimized design for a desired band gap width. Note that this has been so far possible only with numerical optimization repeatedly going back and forth from geometry to the dispersion relation, and hence, it significantly contributes to the overall readability of the system features.