# High-Order Harmonic Generation

The conversion efficiency of gas high-harmonic generation traces a hyperbolic ridge in the pressure–medium-length plane, and standard Bayesian optimization, which models correlations by Euclidean distance, struggles to reproduce that structure. Writing known physical scaling relations into nonlinear coordinate transformations of the search space lets a Gaussian-process surrogate raise structural similarity to a reference grid scan from 0.77 to 0.98 within 60 iterations in two dimensions, and test reconstruction accuracy against 1024 independent reference points in four dimensions. A threshold-based acquisition function then maps extended high-efficiency operating regions rather than a single optimum.

The conversion efficiency of gas high-harmonic generation traces a hyperbolic ridge in the pressure–medium-length plane, and standard Bayesian optimization, which models correlations by Euclidean distance, struggles to reproduce that structure. Writing known physical scaling relations into nonlinear coordinate transformations of the search space lets a Gaussian-process surrogate raise structural similarity to a reference grid scan from 0.77 to 0.98 within 60 iterations in two dimensions, and test reconstruction accuracy against 1024 independent reference points in four dimensions. A threshold-based acquisition function then maps extended high-efficiency operating regions rather than a single optimum.