Accelerating Temperature-Dependent Optical Response Prediction in Truncated Pyramidal GaN/AlN Quantum Dots via Polynomial Ridge Regression

A polynomial Ridge regression model is proposed to accelerate the prediction of temperature-dependent optical responses in a GaN/AlN truncated-pyramidal quantum dot. Reference transition energies were obtained at four temperatures (0, 100, 300, and 500 K) using a combination of coordinate-transformation and finite-difference methods. Leave-one-temperature-out cross-validation was used to select a second-order model with $\lambda =0.178$, yielding an NRMSE of 0.0335 and an $R^2$ of 0.9923. The predictions at 200 and 400 K remain independently unvalidated, whereas comparison with an independent FDM calculation at 600 K gives an absolute transition-energy error of 0.41 meV (0.35%). The reconstructed spectra exhibit the expected temperature-dependent shifts. An inference speed-up of up to $2.66\times {10}^7$ was obtained for three additional temperatures, excluding model training and reference-data generation costs. These predictions have not been independently validated, and the small dataset limits conclusions regarding generalization. The approach is therefore presented as a preliminary surrogate demonstration for the investigated configuration.