  We demonstrate a data-driven method to solve for the invariant probability
density function of a randomly perturbed dynamical system. The key idea is to
replace the boundary condition of numerical schemes by a least squares problem
corresponding to a reference solution, which is generated by Monte Carlo
simulation. With this method we can solve for the invariant probability density
function in any local area with high accuracy, regardless of whether the
attractor is covered by the numerical domain.
