  We present a method for performing data-driven simulations of solar active
region formation and evolution. The approach is based on magnetofriction, which
evolves the induction equation assuming the plasma velocity is proportional to
the Lorentz force. The simulations of active region coronal field are driven by
temporal sequences of photospheric magnetograms from the Helioseismic Magnetic
Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO). Under
certain conditions, the data-driven simulations produce flux ropes that are
ejected from the modeled active region due to loss of equilibrium. Following
the ejection of flux ropes, we find an enhancement of the photospheric
horizontal field near the polarity inversion line. We also present a method for
the synthesis of mock coronal images based on a proxy emissivity calculated
from the current density distribution in the model. This method yields mock
coronal images that are somewhat reminiscent of images of active regions taken
by instruments such as SDO's Atmospheric Imaging Assembly (AIA) at extreme
ultraviolet wavelengths.
