Surrogate modeling of gravitational waves microlensed by spherically symmetric potentials

The anticipated observation of the gravitational microlensing of gravitational waves (GWs) promises to shed light on a host of astrophysical and cosmological questions. However, extracting the parameters of the lens from the modulated GWs requires accurate modeling of the lensing amplification factor, accounting for wave-optics effects. Analytic solutions to the lens equation have not been found to date, except for a handful of simplistic lens models. While numerical solutions to this equation have been developed, the time and computational resources required to evaluate the amplification factor numerically make large-scale parameter estimation of the lens (and source) parameters prohibitive. On the other hand, surrogate modeling of GWs has proven to be a powerful tool to accurately, and rapidly, produce GW templates at arbitrary points in parameter space, interpolating from a finite set of available waveforms at discrete parameter values. In this work, we demonstrate that surrogate modeling can also effectively be applied to the evaluation of the time-domain microlensing amplification factor $\widetilde{F}(t)$. We show this by constructing $\widetilde{F}(t)$ for two lens models, viz. point-mass lens, and singular isothermal sphere, which notably includes logarithmic divergence behaviour. We find both surrogates reproduce the original lens models accurately, with mismatches $\lesssim 5 \times 10^{-4}$ across a range of plausible microlensed binary black hole sources observed by the Einstein Telescope. This surrogate is between 5 and $10^3$ times faster than the underlying lensing models, and can be evaluated in about 100 ms. The accuracy and efficiency attained by our surrogate models will enable practical parameter estimation analyses of microlensed GWs.