Harmonic optimization stops chasing one optimum: physics-based coordinates rebuild the efficiency ridge in 60 iterations
Synopsis
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.
Interpretation
The infrared-to-extreme-ultraviolet conversion efficiency of gas high-harmonic generation peaks along an approximately hyperbolic ridge in the gas-pressure and medium-length plane, a shape previously traced only by direct grid scanning. Conventional Bayesian optimization defines correlations between points by Euclidean distance in parameter space, and in the original pressure–length coordinates it fails to reproduce the hyperbolic structure, yielding a fragmented reconstruction with pronounced vertical bands. Against a conversion-efficiency surface from a direct grid scan, the physics-informed parameterization using logarithmic product–ratio coordinates raised structural similarity to the reference surface from 0.77 in the original coordinates to 0.98 after 60 Bayesian optimization iterations, while all parameterizations reached similar maximum conversion efficiencies.
The gain comes from writing known physical scaling relations directly into the search coordinates rather than from a more elaborate surrogate model. The coordinates first rescale pressure and length by the geometric scaling, then take their product and ratio: the product identifies a particular hyperbola, and the ratio distinguishes pressure–length combinations along it, straightening the curved ridge. In the two-dimensional pressure–length space, five parameterizations each ran 60 iterations against a direct grid-scan reference; in four dimensions, adding laser peak intensity and pulse duration, an independent reference set of 1024 Sobol quasi-random HarP simulations was used, together with inverse-square-root pulse-duration scaling and a square-root transformation of conversion efficiency.
The optimization target shifts from a single optimum to extended high-efficiency operating regions. A conventional acquisition function only pursues points near the current best value, returning isolated extrema. With the Straddle acquisition function, sampling concentrates on the boundary of the region enclosed by a prescribed conversion-efficiency threshold; in two dimensions, normalized root-mean-square error after 60 iterations stayed below the level the authors report for all three thresholds, and structural similarity for the intermediate and highest thresholds also reached the high values they report.
Perspective
The demonstration is limited to HarP numerical simulations of an argon medium driven by a laser at a fixed central wavelength; the two-dimensional study covers gas pressure and medium length, the four-dimensional study adds peak intensity and pulse duration, and optimization is confined to a prescribed parameter domain rather than establishing an absolute maximum conversion efficiency over all physically accessible conditions.
The predicted four-dimensional optimum lies at the upper pressure bound and the lower pulse-duration bound, and the authors state that higher conversion efficiencies beyond these limits cannot be excluded, nor can a different optimal pulse duration in the low-pressure regime. The authors also note that the transformations examined are not necessarily optimal and that alternative transformations remain worth investigating.