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We propose a machine-learning approach based on Bayesian optimization tobuild global potential energy surfaces (PES) for reactive molecular systemsusing feedback from quantum scattering calculations. The method is designed tocorrect for the uncertainties of quantum chemistry calculations and yieldpotentials that reproduce accurately the reaction probabilities in a wide rangeof energies. These surfaces are obtained automatically and do not requiremanual fitting of the {\it ab initio} energies with analytical functions. ThePES are built from a small number of {\it ab initio} points by an iterativeprocess that incrementally samples the most relevant parts of the configurationspace. Using the dynamical results of previous authors as targets, we show thatsuch feedback loops produce accurate global PES with 30 {\it ab initio}energies for the three-dimensional H + H$_2$ $\rightarrow$ H$_2$ + H reactionand 290 {\it ab initio} energies for the six-dimensional OH + H$_2$$\rightarrow$ H$_2$O + H reaction. These surfaces are obtained from 360scattering calculations for H$_3$ and 600 scattering calculations for OH$_3$.We also introduce a method that quickly converges to an accurate PES withoutthe {\it a priori} knowledge of the dynamical results. By construction, ourmethod illustrates the lowest number of potential energy points (i.e. theminimum information) required for the non-parametric construction of global PESfor quantum reactive scattering calculations.

Bayesian optimization for the inverse scattering problem in quantum reaction dynamics