Stability and convergence of the string method for computing minimum energy paths

TL;DR

This paper analyzes the convergence properties of the string method for computing minimum energy paths, demonstrating that with proper initialization and increasing images, the method converges to the true path.

Contribution

It provides a theoretical convergence analysis of the string method, establishing conditions under which it reliably approximates minimum energy paths.

Findings

Convergence to a neighborhood of the minimum energy path is guaranteed under certain assumptions.

Increasing the number of images improves the approximation accuracy.

Proper initialization near the minimum energy path is crucial for convergence.

Abstract

We analyze the convergence of the string method of E, Ren, and Vanden-Eijnden to a minimum energy path. Under some assumptions relating to the critical points on the minimum energy path, we show that the string method initialized in a neighborhood of the minimum energy path converges to an arbitrarily small neighborhood of the minimum energy path as the number of images is increased.