Machine Learning-Driven Prediction of Optical Absorption in Composition-Dependent Truncated Pyramidal GaN/AlxGa1−xN Quantum Dots

Abstract

This study presents a comparative machine-learning investigation for predicting the optical absorption coefficient of truncated pyramidal GaN/AlxGa1−xN quantum dots. The physical dataset is generated by solving the three-dimensional Schrödinger equation using a coordinate-transformation method combined with the finite-difference method (FDM). The coordinate transformation maps the sloping boundaries of the truncated pyramidal geometry onto a regular computational domain, enabling an accurate representation of the quantum-dot shape and facilitating its numerical treatment using the FDM. The absorption coefficient is then calculated as a function of photon energy for different alloy compositions. Using photon energy and alloy composition as input features, Artificial Neural Network (ANN), Random Forest (RFR), Decision Tree (DT), and k-Nearest Neighbor (KNN) models are developed and evaluated. A second-degree polynomial regression model is also considered as a classical baseline. Under the point-wise random 80/20 split, all models show excellent agreement with the numerical results, with R2 values close to unity. KNN generally provides the lowest prediction errors across most alloy compositions, whereas ANN achieves slightly lower MSE and RMSE values at x=0.5. Furthermore, leave-one-composition-out validation identifies ANN as the most effective model for predicting unseen compositions, achieving a mean R2 of 0.848 and an NRMSE of 7.19%. These findings demonstrate that KNN is particularly effective for local interpolation within the sampled domain, while ANN provides stronger composition-wise generalization. The proposed framework offers an efficient surrogate for computationally demanding numerical simulations of the optical properties of quantum nanostructures.