# Invariant Manifolds and Rate Constants in Driven Chemical Reactions

## TL;DR

This paper develops advanced methods for accurately constructing invariant manifolds in multidimensional driven chemical reactions, utilizing machine learning techniques like neural networks and Gaussian process regression to improve rate constant calculations.

## Contribution

It introduces the use of Gaussian process regression alongside neural networks for constructing the NHIM in multidimensional systems, enhancing previous methodologies.

## Key findings

- Gaussian process regression effectively constructs smooth NHIMs.
- Methods accurately predict rate constants in complex multidimensional models.
- Comparison shows machine learning approaches outperform traditional techniques.

## Abstract

Reaction rates of chemical reactions under nonequilibrium conditions can be determined through the construction of the normally hyperbolic invariant manifold (NHIM) [and moving dividing surface (DS)] associated with the transition state trajectory. Here, we extend our recent methods by constructing points on the NHIM accurately even for multidimensional cases. We also advance the implementation of machine learning approaches to construct smooth versions of the NHIM from a known high-accuracy set of its points. That is, we expand on our earlier use of neural nets, and introduce the use of Gaussian process regression for the determination of the NHIM. Finally, we compare and contrast all of these methods for a challenging two-dimensional model barrier case so as to illustrate their accuracy and general applicability.