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The period of pulsation and the structure of the light curve for Cepheid andRR Lyrae variables depend on the fundamental parameters of the star: mass,radius, luminosity, and effective temperature. Here we train artificial neuralnetworks on theoretical pulsation models to predict the fundamental parametersof these stars based on their period and light curve structure. We findsignificant improvements to estimates of these parameters made using lightcurve structure and period over estimates made using only the period. Giventhat the models are able to reproduce most observables, we find that thefundamental parameters of these stars can be estimated up to 60% moreaccurately when light curve structure is taken into consideration. We quantifywhich aspects of light curve structure are most important in determiningfundamental parameters, and find for example that the second Fourier amplitudecomponent of RR Lyrae light curves is even more important than period indetermining the effective temperature of the star. We apply this analysis toobservations of hundreds Cepheids in the Large Magellanic Cloud and thousandsof RR Lyrae in the Magellanic Clouds and Galactic bulge to produce catalogs ofestimated masses, radii, luminosities, and other parameters of these stars. Asan example application, we estimate Wesenheit indices and use those to derivedistance moduli to the Magellanic Clouds of $\mu_{\text{LMC},\text{CEP}} =18.688 \pm 0.093$, $\mu_{\text{LMC},\text{RRL}} = 18.52 \pm 0.14$, and$\mu_{\text{SMC},\text{RRL}} = 18.88 \pm 0.17$ mag.

When a Period Is Not a Full Stop: Light Curve Structure Reveals Fundamental Parameters of Cepheid and RR Lyrae Stars