  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.
