.Noise-induced transitions between multistable states happen in a multitude of systems, such as species extinction in biology, protein folding, or tipping points in climate science. Large deviation theory is the rigorous language to describe such transitions for nonequilibrium systems in the small noise limit. At its core, it requires the computation of the most likely transition pathway, solution to a PDE constrained optimization problem. Standard methods struggle to compute the minimizer in the particular coexistence of (1) multistability, i.e., coexistence of multiple long-lived states, and (2) degenerate noise, i.e., stochastic forcing acting only on a small subset of the system's degrees of freedom. In this paper, we demonstrate how to adapt existing methods to compute the large deviation minimizer in this setting by combining ideas from optimal control, large deviation theory, and numerical optimization. We show the efficiency of the introduced method in various applications in biology, medicine, and fluid dynamics, including the transition to turbulence in subcritical pipe flow.Keywordsstochastic partial differential equationsFreidlin–Wentzell theorymetastabilitydegenerate noisetransition to turbulenceMSC codes60H1565C5065Z0582B26
Bernuzzi et al. (Wed,) studied this question.