  A novel method for investigating the sensitivity of the tip of the red giant
branch (TRGB) I band magnitude $M_I$ to stellar input physics is presented. We
compute a grid of $\sim$125,000 theoretical stellar models with varying mass,
initial helium abundance, and initial metallicity, and train a machine learning
emulator to predict $M_I$ as a function of these parameters. First, our
emulator can be used to theoretically predict $M_I$ in a given galaxy using
Monte Carlo sampling. As an example, we predict $M_I = -3.84^{+0.14}_{-0.12}$
in the Large Magellanic Cloud. Second, our emulator enables a direct comparison
of theoretical predictions for $M_I$ with empirical calibrations to constrain
stellar modeling parameters using Bayesian Markov Chain Monte Carlo methods. We
demonstrate this by using empirical TRGB calibrations to obtain new independent
measurements of the metallicity in three galaxies. We find
$Z=0.0117^{+0.0083}_{-0.0055}$ in the Large Magellanic Cloud,
$Z=0.0077^{+0.0074}_{-0.0038}$ in NGC 4258, and $Z=0.0111^{+0.0083}_{-00.0056}$
in $\omega$-Centauri, consistent with other measurements. Other potential
applications of our methodology are discussed.
