Predicting trajectory behaviour via machine-learned invariant manifolds

Vladimír Krajňák; Shibabrat Naik; Stephen Wiggins

doi:10.1016/j.cplett.2021.139290

Predicting trajectory behaviour via machine-learned invariant manifolds

Vladimír Krajňák^*, Shibabrat Naik^*, Stephen Wiggins^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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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
Hamiltonian.

Original language	English
Article number	139290
Journal	Chemical Physics Letters: X
Volume	789
Early online date	30 Dec 2021
DOIs	https://doi.org/10.1016/j.cplett.2021.139290
Publication status	Published - 1 Feb 2022

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title = "Predicting trajectory behaviour via machine-learned invariant manifolds",

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{\textquoteright}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{\textquoteright}s Hamiltonian.",

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N2 - 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 Hamiltonian.

AB - 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 Hamiltonian.

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DO - 10.1016/j.cplett.2021.139290

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Predicting trajectory behaviour via machine-learned invariant manifolds

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