Bayesian optimization for the inverse scattering problem in quantum reaction dynamics

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 ab initio energies with analytical functions. The PES are built from a small number of 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 ab initio energies for the three-dimensional H + H _2 $\to $ H _2 + H reaction and 290 ab inito energies for the six-dimensional OH + H _2 $\to $ 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 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.

Keywords

• bayesian optimization
• gaussian processes
• inverse scattering problem