Abstract

We present a Gaussian-process (GP) surrogate model for the normal-incidence reflectance spectrum R(λ) of one-dimensional GaAs/Al0.3Ga0.7As distributed Bragg reflectors (DBRs). A Latin-hypercube dataset of 1500 transfer-matrix-method (TMM) simulations spanning Nperiods ∈[5, 20], tGaAs ∈[50, 200] nm, and tAlGaAs ∈[50, 200] nm over the 900–1100 nm window is used to train and evaluate the model. Principal component analysis (PCA) reduces the 150-point spectral output to 26 components (≥99.9% variance retained); one GP is fitted per component. On a held-out test set (n = 150) the GP achieves RMSE = 0.085 and R₂ = 0.276, while a Random Forest (RF) baseline reaches RMSE = 0.065 and R₂ = 0.572. GP inference is 4.4 ms per spectrum compared with ∼308 ms for TMM, yielding a ∼70× speedup. Uncertainty calibration shows that the GP 95% prediction band covers 98.9% of test residuals, indicating conservative but reliable uncertainty estimates. These results establish a rapid surrogate for DBR design-space exploration and motivate further work on sparse or inducing-point GP formulations to close the accuracy gap with the <0.02 RMSE target.

Abstract

We present a Gaussian-process (GP) surrogate model for the normal-incidence reflectance spectrum R(λ) of one-dimensional GaAs/Al0.3Ga0.7As distributed Bragg reflectors (DBRs). A Latin-hypercube dataset of 1500 transfer-matrix-method (TMM) simulations spanning Nperiods ∈[5, 20], tGaAs ∈[50, 200] nm, and tAlGaAs ∈[50, 200] nm over the 900–1100 nm window is used to train and evaluate the model. Principal component analysis (PCA) reduces the 150-point spectral output to 26 components (≥99.9% variance retained); one GP is fitted per component. On a held-out test set (n = 150) the GP achieves RMSE = 0.085 and R₂ = 0.276, while a Random Forest (RF) baseline reaches RMSE = 0.065 and R₂ = 0.572. GP inference is 4.4 ms per spectrum compared with ∼308 ms for TMM, yielding a ∼70× speedup. Uncertainty calibration shows that the GP 95% prediction band covers 98.9% of test residuals, indicating conservative but reliable uncertainty estimates. These results establish a rapid surrogate for DBR design-space exploration and motivate further work on sparse or inducing-point GP formulations to close the accuracy gap with the <0.02 RMSE target.

Abstract

We present a Gaussian-process (GP) surrogate model for the normal-incidence reflectance spectrum R(λ) of one-dimensional GaAs/Al0.3Ga0.7As distributed Bragg reflectors (DBRs). A Latin-hypercube dataset of 1500 transfer-matrix-method (TMM) simulations spanning Nperiods ∈[5, 20], tGaAs ∈[50, 200] nm, and tAlGaAs ∈[50, 200] nm over the 900–1100 nm window is used to train and evaluate the model. Principal component analysis (PCA) reduces the 150-point spectral output to 26 components (≥99.9% variance retained); one GP is fitted per component. On a held-out test set (n = 150) the GP achieves RMSE = 0.085 and R₂ = 0.276, while a Random Forest (RF) baseline reaches RMSE = 0.065 and R₂ = 0.572. GP inference is 4.4 ms per spectrum compared with ∼308 ms for TMM, yielding a ∼70× speedup. Uncertainty calibration shows that the GP 95% prediction band covers 98.9% of test residuals, indicating conservative but reliable uncertainty estimates. These results establish a rapid surrogate for DBR design-space exploration and motivate further work on sparse or inducing-point GP formulations to close the accuracy gap with the <0.02 RMSE target.

Abstract

We present a Gaussian-process (GP) surrogate model for the normal-incidence reflectance spectrum R(λ) of one-dimensional GaAs/Al0.3Ga0.7As distributed Bragg reflectors (DBRs). A Latin-hypercube dataset of 1500 transfer-matrix-method (TMM) simulations spanning Nperiods ∈[5, 20], tGaAs ∈[50, 200] nm, and tAlGaAs ∈[50, 200] nm over the 900–1100 nm window is used to train and evaluate the model. Principal component analysis (PCA) reduces the 150-point spectral output to 26 components (≥99.9% variance retained); one GP is fitted per component. On a held-out test set (n = 150) the GP achieves RMSE = 0.085 and R₂ = 0.276, while a Random Forest (RF) baseline reaches RMSE = 0.065 and R₂ = 0.572. GP inference is 4.4 ms per spectrum compared with ∼308 ms for TMM, yielding a ∼70× speedup. Uncertainty calibration shows that the GP 95% prediction band covers 98.9% of test residuals, indicating conservative but reliable uncertainty estimates. These results establish a rapid surrogate for DBR design-space exploration and motivate further work on sparse or inducing-point GP formulations to close the accuracy gap with the <0.02 RMSE target.