  Sampling rare events in metastable dynamical systems is often a
computationally expensive task and one needs to resort to enhanced sampling
methods such as importance sampling. Since we can formulate the problem of
finding optimal importance sampling controls as a stochastic optimization
problem, this then brings additional numerical challenges and the convergence
of corresponding algorithms might as well suffer from metastabilty. In this
article, we address this issue by combining systematic control approaches with
the heuristic adaptive metadynamics method. Crucially, we approximate the
importance sampling control by a neural network, which makes the algorithm in
principle feasible for high-dimensional applications. We can numerically
demonstrate in relevant metastable problems that our algorithm is more
effective than previous attempts and that only the combination of the two
approaches leads to a satisfying convergence and therefore to an efficient
sampling in certain metastable settings.
