  We present a methodology for constructing modified gravity (MG) constrained
simulations of the local Universe using positions and peculiar velocities from
the CosmicFlows data set. Our analysis focuses on the following MG models: the
normal branch of the Dvali-Gabadadze-Porrati (nDGP) model and Hu-Sawicki $f(R)$
model. We develop a model independent methodology for constructing constrained
simulations with any given power spectra and numerically calculated linear
growth functions. Initial conditions (ICs) for a set of constrained simulations
are constructed for the standard cosmological model $\Lambda$CDM and the MG
models. Differences between the model's reconstructed Wiener filtered density
and the resultant simulation density are presented showing the importance for
the generation of MG constrained ICs to study the subtle effects of MG in the
local Universe. These are the first MG constrained simulations ever produced.
The current work paves the way to improved approximate methods for models with
scale-dependent growth functions, such as $f(R)$, and for high-resolution
hydrodynamical MG zoom-in simulations of the local Universe.
