# Predicting trajectory behaviour via machine-learned invariant manifolds

arXiv: https://arxiv.org/abs/2107.10154 · HTML: https://mlsanity.com/paper/2107.10154/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 55 references that are in the map.
- First posted on arXiv 21 Jul 2021.

## Builds on (most cited first, 4 of 4)

- [Machine learning for molecular simulation](https://mlsanity.com/paper/1911.02792/) (2019)
- [OrbNet: Deep Learning for Quantum Chemistry Using Symmetry-Adapted Atomic-Orbital Features](https://mlsanity.com/paper/2007.08026/) (2020)
- [Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds](https://mlsanity.com/paper/1904.08622/) (2019)
- [Support vector machines for learning reactive islands](https://mlsanity.com/paper/2107.08429/) (2021)

## Built on by (most cited first, 1 of 1)

- [Learning effective dynamics from data-driven stochastic systems](https://mlsanity.com/paper/2205.04151/) (2022)

## Abstract (arXiv)

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 CH4^+ Hamiltonian.