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Gravitational wave observations of binary black holes have revealedunexpected structure in the black hole mass distribution. Previous studies ofthe mass distribution employ physically-motivated phenomenological models andinfer the parameters that directly control the features of the massdistribution that are allowed in their model, associating the constraints onthose parameters with their physical motivations. In this work, we take analternative approach in which we introduce a model parameterizing theunderlying stellar and core-collapse physics and obtaining the remnant blackhole distribution as a derived byproduct. In doing so, we directly constrainthe stellar physics necessary to explain the astrophysical distribution ofblack hole properties under a given model. We apply this approach to modelingthe mapping between stellar core mass and remnant black hole mass, includingthe effects of mass loss due to the pulsational pair instability supernova(PPISN) process, which has been proposed as an explanation for the observedexcess of black holes at $\sim 35 M_\odot$. Placing constraints on the nuclearreaction rates necessary to explain the PPISN parameters, we conclude that thepeak observed at $\sim 35 M_\odot$ is highly unlikely to be a signature fromthe PPISN process. This procedure can be applied to modeling any physicalprocess that underlies the astrophysical mass distribution. Allowing theparameters of the core-remnant mass relationship to evolve with redshiftpermits correlated and physically reasonable changes in the location, shape,and amplitude of features in the mass function. We find that the current dataare consistent with no redshift evolution in the core-remnant massrelationship, but ultimately place only weak constraints on the change of theseparameters.

Physical Models for the Astrophysical Population of Black Holes: Application to the Bump in the Mass Distribution of Gravitational Wave Sources