Predicting trajectory behaviour via machine-learned invariant manifolds
This work addresses the challenge of predicting trajectory behavior in high-dimensional or computationally expensive systems, offering an incremental improvement over existing methods.
The paper tackled the problem of distinguishing distinct reaction pathways in dynamical systems by developing a machine learning framework using support vector machines (SVM) to discover phase space structures from trajectory data, achieving computational efficiency with minimal a priori knowledge and benchmarking on Chesnavich's CH4+ Hamiltonian.
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.