This article introduces a framework to supplement short historical catalogs with synthetic catalogs and determine large earthquakes’ recurrence. For this assessment, we developed a parameter estimation technique for a probabilistic earthquake occurrence model that captures time and space interactions between large mainshocks. The technique is based on a two‐step Bayesian update that uses a synthetic catalog from physics‐based simulations for initial parameter estimation and then the historical catalog for further calibration, fully characterizing parameter uncertainty. The article also provides a formulation to combine multiple synthetic catalogs according to their likelihood of representing empirical earthquake stress drops and Global Positioning System‐inferred interseismic coupling. We applied this technique to analyze large‐magnitude earthquakes’ recurrence along 650 km of the subduction fault’s interface located offshore Lima, Peru. We built nine 2000 yr long synthetic catalogs using quasi‐dynamic earthquake cycle simulations based on the rate‐and‐state friction law to supplement the 450 yr long historical catalog. When the synthetic catalogs are combined with the historical catalog without propagating their uncertainty, we found average relative reductions larger than 90% in the recurrence parameters’ uncertainty. When we propagated the physics‐based simulations’ uncertainty to the posterior, the reductions in uncertainty decreased to 60%–70%. In two Bayesian assessments, we then show that using synthetic catalogs results in higher parameter uncertainty reductions than using only the historical catalog (69% vs. 60% and 83% vs. 80%), demonstrating that synthetic catalogs can be effectively combined with historical data, especially in tectonic regions with short historical catalogs. Finally, we show the implications of these results for time‐dependent seismic hazard.