  The study of noise-driven transitions occurring rarely on the time-scale of
systems modeled by SDEs is of crucial importance for understanding such
phenomena as genetic switches in living organisms and magnetization switches of
the Earth. For a gradient SDE, the predictions for transition times and paths
between its metastable states are done using the potential function. For a
nongradient SDE, one needs to decompose its forcing into a gradient of the
so-called quasipotential and a rotational component, which cannot be done
analytically in general.
  We propose a methodology for computing the quasipotential for highly
dissipative and chaotic systems built on the example of Lorenz'63 with an added
stochastic term. It is based on the ordered line integral method, a
Dijkstra-like quasipotential solver, and combines 3D computations in whole
regions, a dimensional reduction technique, and 2D computations on radial
meshes on manifolds or their unions. Our collection of source codes is
available on M. Cameron's web page and on GitHub.
