We present a numerical framework for the variability of active galactic nuclei (AGN), which links the variability of AGN over a broad range of timescales and luminosities to the observed properties of the AGN population as a whole, and particularly the Eddington ratio distribution function (ERDF). We have implemented our framework on GPU architecture, relying on previously published time series generating algorithms. After extensive tests that characterise several intrinsic and numerical aspects of the simulations, we describe some applications used for current and future time domain surveys and for the study of extremely variable sources (e.g., changing look or flaring AGN). Specifically, we define a simulation setup which reproduces the AGN variability observed in the PTF/iPTF survey, and use it to forward model longer light curves of the kind that may be observed within the LSST main survey. Thanks to our effcient implementations, these simulations are able to cover for example over 1 Myr with a roughly weekly cadence. We envision that this framework will become highly valuable to prepare for, and best exploit, data from upcoming time domain surveys, such as for example LSST.
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