Bayesian optimization for the inverse scattering problem in quantum reaction dynamics

TL;DR

This paper introduces a Bayesian optimization-based machine learning method to efficiently construct accurate global potential energy surfaces for reactive molecular systems, reducing the number of ab initio points needed.

Contribution

The authors develop an iterative, feedback-driven approach that automatically builds global PES with minimal ab initio data, improving efficiency over traditional fitting methods.

Findings

Achieved accurate PES with only 30 ab initio points for H + H2 reaction.

Constructed PES with 290 ab initio points for OH + H2 reaction.

Performed hundreds of scattering calculations to validate the PES accuracy.

Abstract

We propose a machine-learning approach based on Bayesian optimization to build global potential energy surfaces (PES) for reactive molecular systems using feedback from quantum scattering calculations. The method is designed to correct for the uncertainties of quantum chemistry calculations and yield potentials that reproduce accurately the reaction probabilities in a wide range of energies. These surfaces are obtained automatically and do not require manual fitting of the {\it ab initio} energies with analytical functions. The PES are built from a small number of {\it ab initio} points by an iterative process that incrementally samples the most relevant parts of the configuration space. Using the dynamical results of previous authors as targets, we show that such feedback loops produce accurate global PES with 30 {\it ab initio} energies for the three-dimensional H + H$_2$ $\rightarrow$ H$_2$ + H reaction and 290 {\it ab initio} energies for the six-dimensional OH + H$_2$ $\rightarrow$ H$_2$O + H reaction. These surfaces are obtained from 360 scattering calculations for H$_3$ and 600 scattering calculations for OH$_3$. We also introduce a method that quickly converges to an accurate PES without the {\it a priori} knowledge of the dynamical results. By construction, our method illustrates the lowest number of potential energy points (i.e. the minimum information) required for the non-parametric construction of global PES for quantum reactive scattering calculations.