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Observations of exoplanetary systems provide clues about the intrinsicdistribution of planetary systems, their architectures, and how they formed. Wedevelop a forward modelling framework for generating populations of planetarysystems and "observed" catalogues by simulating the Kepler detection pipeline(SysSim). We compare our simulated catalogues to the Kepler DR25 catalogue ofplanet candidates, updated to include revised stellar radii from Gaia DR2. Weconstrain our model based on the observed 1D marginal distributions of orbitalperiods, period ratios, transit depths, transit depth ratios, transitdurations, transit duration ratios, and transit multiplicities. Models assumingplanets with independent periods and sizes do not adequately account for theproperties of the multiplanet systems. Instead, a clustered point process modelfor exoplanet periods and sizes provides a significantly better description ofthe Kepler population, particularly the observed multiplicity and period ratiodistributions. We find that $0.56^{+0.18}_{-0.15}$ of FGK stars have at leastone planet larger than $0.5 R_\oplus$ between 3 and 300 d. Most of theseplanetary systems ($\sim 98\%$) consist of one or two clusters with a median ofthree planets per cluster. We find that the Kepler dichotomy is evidence for apopulation of highly inclined planetary systems and is unlikely to be solelydue to a population of intrinsically single planet systems. We provide a largeensemble of simulated physical and observed catalogues of planetary systemsfrom our models, as well as publicly available code for generating similarcatalogues given user-defined parameters.

Architectures of Exoplanetary Systems. I: A Clustered Forward Model for Exoplanetary Systems around Kepler's FGK Stars