  Computing the invariant probability measure of a randomly perturbed dynamical
system usually means solving the stationary Fokker-Planck equation. This paper
studies several key properties of a novel data-driven solver for
low-dimensional Fokker-Planck equations proposed in [15]. Based on these
results, we propose a new `block solver' for the stationary Fokker-Planck
equation, which significantly improves the performance of the original
algorithm. Some possible ways of reducing numerical artifacts caused by the
block solver are discussed and tested with examples.
