Surrogate modeling of intersubband nonlinear optical spectra in GaAs/AlGaAs double quantum wells: a systematic benchmark

Abstract

Accurate modeling of nonlinear optical responses in semiconductor quantum wells demands repeated, computationally expensive solutions of the Schrödinger equation across wide structural and field parameter spaces. Here we present a physics-informed surrogate framework combining an effective-mass density-matrix baseline with three data-driven correctors and provide a systematic benchmark on a stratified held-out test set of 1,620 configurations (540 per geometry). Three confinement profiles—square, graded, and parabolic—are studied under applied electric and magnetic fields using a dataset of 10,800 configurations computed with the full eight-subband reference solver. For optical rectification, the three-subband baseline achieves a relative root-mean-square error of 5.2±7.1%, demonstrating that three subbands fully capture the dominant response; no surrogate model improves upon this. For second harmonic generation (SHG), MLP and Ridge Regression reduce the baseline relative RMSE from 11.7±3.8% to 4.9±2.7% and 5.7±3.8% (65.7% and 61.9% reductions; p<0.001, Cohen’s d>1.0). The kernel-ridge corrector with random Fourier features also improves SHG by 48.4% ( d=0.80). A Gaussian process regression baseline (implemented via kernel ridge regression with PCA compression) achieves 46.5% improvement, confirming that the learnable SHG signal is accessible to multiple regressor families. A principal component analysis of the log-domain residuals r=log10⁡|sref|−log10⁡|s^ph| reveals that the OR truncation error carries limited learnable signal (total residual variance 0.27log-unit2), rationalizing why surrogate correction is counterproductive for OR; the SHG residual is 3.1× larger and structurally richer, enabling the observed surrogate improvements. A hyperparameter sensitivity study confirms the robustness of the chosen architectures. These physically interpretable results provide architecture-selection guidance and a 6.0-fold inference speedup over the full reference solver.