A Concerted Variational Strategy for Investigating Rare Events

TL;DR

This paper introduces a variational approach based on Hamilton's principle and the Maupertuis principle, combined with a saddle point algorithm, to effectively identify transition paths between stable states in complex systems.

Contribution

It presents a novel variational strategy that transforms Hamilton's principle into a minimum problem with constraints, improving the search for rare event transition paths.

Findings

The method effectively finds transition paths connecting stable basins.

The saddle point algorithm efficiently converges to true solutions.

Using Maupertuis principle refines transition time estimation.

Abstract

A strategy for finding transition paths connecting two stable basins is presented. The starting point is the Hamilton principle of stationary action; we show how it can be transformed into a minimum principle through the addition of suitable constraints like energy conservation. Methods for improving the quality of the paths are presented: for example, the Maupertuis principle can be used for determining the transition time of the trajectory and for coming closer to the desired dynamic path. A saddle point algorithm (conjugate residual method) is shown to be efficient for reaching a ``true'' solution of the original variational problem.