Physics-based phenomenological modeling of binary black hole hierarchical formation 2: Autodifferentiable functional inference of hierarchical compact-binary populations
The gravitational-wave (GW) census contains mass and spin structure consistent with contributions from black holes assembled through repeated mergers in dense environments. Connecting that structure to formation physics requires models that are both physically interpretable and tractable within population inference. We construct an autodifferentiable, physics-based phenomenological model in which each dense environment is represented by a coagulation response and a population of such environments produces an observable merger-rate density. Embedded in the gwkokab Poisson-likelihood framework, this model enables joint inference of natal-population and interaction parameters from the GW census. Applied to GWTC-5.0, the framework shows why simple pairwise coagulation models struggle to reproduce the observed high-mass, comparable-mass population and tests alternative interaction structures against the data, while retaining an explicitly modeled natal component.