Predicting trajectory behaviour via machine-learned invariant manifolds

TL;DR

This paper introduces a machine learning framework using support vector machines to identify phase space structures that differentiate reaction pathways, especially effective in high-dimensional or computationally expensive systems.

Contribution

The authors develop a novel SVM-based method that requires minimal prior knowledge and fewer trajectories, improving efficiency over existing techniques for complex Hamiltonian systems.

Findings

Effective in high-dimensional systems

Requires fewer trajectories for training

Benchmark results on Chesnavich's Hamiltonian

Abstract

In this paper, we use support vector machines (SVM) to develop a machine learning framework to discover phase space structures that distinguish between distinct reaction pathways. The SVM model is trained using data from trajectories of Hamilton's equations and works well even with relatively few trajectories. Moreover, this framework is specifically designed to require minimal a priori knowledge of the dynamics in a system. This makes our approach computationally better suited than existing methods for high-dimensional systems and systems where integrating trajectories is expensive. We benchmark our approach on Chesnavich's CH$_4^+$ Hamiltonian.