Emulating distributions of planetary system architectures

Inferring the distribution of exoplanetary system architectures from survey data increasingly relies on forward modeling with N -body simulations, but the computational cost of these models makes rigorous statistical inference impractical. We develop a statistical emulator for the distribution of outcomes of planet formation simulations, enabling fast conditional sampling in place of expensive integrations. The emulator targets the joint distribution of detected multiplicity and three observables derived from neighboring planet pairs: orbital period ratios, period-normalized transit duration ratios, and orbital spacing in mutual Hill radii. Our approach combines a calibrated model for multiplicity, flexible regression models for conditional distributions, dependence modeling in a transformed probability space, and methods to capture rare events in the tails. We introduce diagnostics to assess calibration, dependence preservation, and reproduction of rare events. The resulting emulator accurately captures heteroskedasticity, dependence structure, and tail behavior of the simulator outputs while reducing computational cost by several orders of magnitude relative to direct N -body simulation. This framework enables integration of detailed dynamical models into simulation-based inference for exoplanet populations.