In the context of space weather forecasting, solar EUV irradiance
specification is needed on multiple time scales, with associated
uncertainty quantification for determining the accuracy of downstream
parameters. Empirical models of irradiance often rely on parametric fits
between irradiance in several bands and various solar indices. We build
upon these empirical models by using Generalized Additive Models (GAMs)
to represent solar irradiance. We apply the GAM approach in two steps:
(1) A GAM is between FISM2 irradiance and solar indices F10.7, Revised
Sunspot Number, and the Lyman-alpha solar index. (2) A second GAM is fit
to model the residuals of the first GAM with respect to TIMED/SEE
irradiance. We evaluate the performance of this approach during Solar
Cycle 24 and compare it with FISM2, and show that mean relative
irradiance error for integrated solar EUV irradiance is decreased from
-3.459% for FISM2 to 0.04% using GAMs driven by known solar indices
with a small increase in variance. We demonstrate negligible dependence
of performance on solar cycle and season, and we assess the efficacy of
the GAM approach across different wavelengths.