Analysing kinetic transition networks for rare events

TL;DR

This paper compares graph transformation and linear algebra methods for analyzing kinetic transition networks, demonstrating that graph transformation is more robust in rare event scenarios with large, sparse networks.

Contribution

It introduces a robust graph transformation approach for computing kinetic network properties, outperforming traditional linear algebra methods in rare event and large sparse network cases.

Findings

Graph transformation outperforms linear algebra in robustness.

Graph transformation succeeds where other methods fail due to numerical issues.

Effective for analyzing rare event dynamics in large, sparse networks.

Abstract

The graph transformation approach is a recently proposed method for computing mean first passage times, rates, and committor probabilities for kinetic transition networks. Here we compare the performance to existing linear algebra methods, focusing on large, sparse networks. We show that graph transformation provides a much more robust framework, succeeding when numerical precision issues cause the other methods to fail completely. These are precisely the situations that correspond to rare event dynamics for which the graph transformation was introduced.