Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics

TL;DR

This paper introduces a novel method combining control approaches with adaptive metadynamics to improve importance sampling for rare event simulation in high-dimensional metastable systems, demonstrating enhanced efficiency and convergence.

Contribution

The paper proposes integrating neural network-based control approximation with adaptive metadynamics to address metastability challenges in importance sampling.

Findings

The combined method outperforms previous approaches in metastable sampling tasks.

Neural network control approximation enables application to high-dimensional systems.

The approach achieves better convergence and sampling efficiency in numerical experiments.

Abstract

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.