Classifying the generation and formation channels of individual LIGO-Virgo-KAGRA observations from dynamically formed binaries

We address two important questions in gravitational-wave astronomy. What is the astrophysical formation scenario leading to black-hole binary mergers? Did some of the merging black holes form hierarchically through previous generations of mergers? Leveraging fast-to-generate astrophysical simulations from the rapster code and a random forest algorithm, we develop a pipeline to accurately classify the most likely generation and formation scenario of dynamically formed BHs on an event-by-event basis. We test our framework on four merger events with features suggesting a dynamical origin: the large total mass event GW190521, GW190412 (with large mass asymmetry), and two events with effective spins antialigned with the orbital angular momentum (GW191109 and GW200225). Within the models we consider, and assuming these events to be formed dynamically, we find that one of the component black holes in GW190521 formed from a previous merger with high probability ($\gtrsim 85\%$). GW190521, GW191109 and GW200225 are compatible with formation through three-body interactions, while the most likely formation channel for GW190412 are two-body captures. We also rule out that GW191109 contains only first-generation black holes with a probability of 97$\%$. Our pipeline could be useful to identify the evolutionary path of individual GW observations once it is trained on more comprehensive sets of binary formation simulations.