Fitting planet formation models to the exoplanet demographics necessitates to generate hundred of thousands of systems. Yet, modelling every planet formation processes,such as dust coagulation, interactions with the protoplanetary disk or planet interactions, in a single simulation is still beyond our computational capabilities. The population synthesis approach aims at combining fast semi-analytical recipes modelling the important physical processes at play, to keep an affordable computational cost. The bottleneck of the current state-of-the-art simulations is the N-body interactions between planetary embryos, within and after the disk lifetime. In this work we propose a framework to replace direct N-body integrations in population synthesis models by semi-analytical recipes derived from the recent breakthroughs in our understanding of planet dynamics during their formation. We self-consistently model mean motion resonances, compact systems instability, planet scattering and collisions. We combine our model with state-of-the-art modelling of planet growth and migration. Our method statistically reproduces results obtained in simulations including N-body integration, for a fraction of the computational cost. We discuss how this approach enable us to use the entire exoplanet population to constrain planet formation models and planetary system architecture.