Benchmarking machine-learning surrogates for rapid prediction of the reflectance-defined stopband width of finite dielectric Bragg reflectors
Abstract
Predicting the stopband width of finite one-dimensional dielectric Bragg reflectors requires a transfer-matrix calculation followed by spectrum-level edge extraction for each candidate stack. Although an individual wavelength-vectorized TMM evaluation is inexpensive, this calculation is repeated throughout large screening campaigns. Five supervised regressors are benchmarked as surrogates for the reflectance-defined stopband width ΔλStop of finite multilayers at normal incidence, in the lossless, non-dispersive limit. TMM spectra were generated for stacks parameterized by the refractive indices nL and nH, the layer thicknesses dL and dH, and the number of bilayers N. For each spectrum, ΔλStop was taken as the widest continuous interval with R(λ) ≥ 0.95. Designs with no such interval, or with a widest interval below 5 nm, were excluded, retaining 1660 of 2000 sampled designs. Hyperparameters of RF and SVR were selected by 10-fold cross-validation on the 1411-structure development set, while MLP depth was examined from one to ten hidden layers under the same test-isolated protocol. The selected six-hidden-layer MLP (128,64,32,16,16,16) achieved R2 = 0.9862, RMSE = 10.47 nm, and MAE = 5.92 nm on the independent 249-structure test set. On a structured external set of 120 quarter-wave designs from four dielectric pairs, the final MLP achieved R2 = 0.9688, RMSE = 5.67 nm, and MAE = 4.44 nm against the TMM reference; 94.17% of the cases had absolute errors below 10 nm and all 120 cases remained below 20 nm. Under an accuracy-controlled benchmark, the wavelength-vectorized TMM required 0.856 ms per structure at the selected 201-point spectral grid, whereas end-to-end single-sample inference with the final MLP, including input standardization, required 0.328 ms, corresponding to a 2.60× speedup. The surrogate is intended as a bounded-domain screening tool complementing, not replacing, full TMM analysis.
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BibTeX
@article{bouazzi2026benchmarking,
title = {{Benchmarking machine-learning surrogates for rapid prediction of the reflectance-defined stopband width of finite dielectric Bragg reflectors}},
author = {Yassine Bouazzi and Mohamed Saleh M. Esmail and Mabrouk Touahmia and Zied Elleuch and Serhan Alshammari and Foued Selmi and Mounir Kanzari and Hiba Bouandas and Sayed El. Soliman},
journal = {Scientific Reports},
year = {2026},
month = oct,
doi = {10.1038/s41598-026-75942-x},
url = {https://www.nature.com/articles/s41598-026-75942-x},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - Benchmarking machine-learning surrogates for rapid prediction of the reflectance-defined stopband width of finite dielectric Bragg reflectors
AU - Yassine Bouazzi
AU - Mohamed Saleh M. Esmail
AU - Mabrouk Touahmia
AU - Zied Elleuch
AU - Serhan Alshammari
AU - Foued Selmi
AU - Mounir Kanzari
AU - Hiba Bouandas
AU - Sayed El. Soliman
PY - 2026
DA - 2026/10/23
JO - Scientific Reports
DO - 10.1038/s41598-026-75942-x
UR - https://www.nature.com/articles/s41598-026-75942-x
AB - Predicting the stopband width of finite one-dimensional dielectric Bragg reflectors requires a transfer-matrix calculation followed by spectrum-level edge extraction for each candidate stack. Although an individual wavelength-vectorized TMM evaluation is inexpensive, this calculation is repeated throughout large screening campaigns. Five supervised regressors are benchmarked as surrogates for the reflectance-defined stopband width ΔλStop of finite multilayers at normal incidence, in the lossless, non-dispersive limit. TMM spectra were generated for stacks parameterized by the refractive indices nL and nH, the layer thicknesses dL and dH, and the number of bilayers N. For each spectrum, ΔλStop was taken as the widest continuous interval with R(λ) ≥ 0.95. Designs with no such interval, or with a widest interval below 5 nm, were excluded, retaining 1660 of 2000 sampled designs. Hyperparameters of RF and SVR were selected by 10-fold cross-validation on the 1411-structure development set, while MLP depth was examined from one to ten hidden layers under the same test-isolated protocol. The selected six-hidden-layer MLP (128,64,32,16,16,16) achieved R2 = 0.9862, RMSE = 10.47 nm, and MAE = 5.92 nm on the independent 249-structure test set. On a structured external set of 120 quarter-wave designs from four dielectric pairs, the final MLP achieved R2 = 0.9688, RMSE = 5.67 nm, and MAE = 4.44 nm against the TMM reference; 94.17% of the cases had absolute errors below 10 nm and all 120 cases remained below 20 nm. Under an accuracy-controlled benchmark, the wavelength-vectorized TMM required 0.856 ms per structure at the selected 201-point spectral grid, whereas end-to-end single-sample inference with the final MLP, including input standardization, required 0.328 ms, corresponding to a 2.60× speedup. The surrogate is intended as a bounded-domain screening tool complementing, not replacing, full TMM analysis.
SN - 2045-2322
ER -