This study investigates the electronic and nonlinear optical properties of coupled GaN/AlN quantum dots using a numerical approach based on coordinate transformation combined with the finite difference method (FDM). The Schrödinger equation is solved to determine the electronic energy levels and wave functions of the system, which are subsequently used to evaluate the nonlinear optical rectification (NOR) response. Since numerical simulations become computationally expensive for large quantum dot systems, several regression-based models, including Polynomial Regression, Ridge Regression, LASSO, and Elastic Net, are trained on high-fidelity numerical data. These models learn the relationship between structural parameters and the resulting electronic and optical properties, enabling fast and reliable predictions for larger quantum dot configurations. The predictive performance of the ML models is assessed by comparing their results with the numerical simulations, showing excellent agreement while significantly reducing computational effort. The proposed hybrid physics–machine learning framework therefore provides an efficient and reliable approach for predicting the electronic and nonlinear optical behavior of coupled GaN/AlN quantum dots.
Brahim et al. (Sun,) studied this question.