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  H 2 + H reaction and 290 ab inito energies for the six-dimensional OH + H 2  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.

Automatically growing global reactive neural network potential energy surfaces: A trajectory-free active learning strategy

“…We note in passing that the number of random initial guesses in the LM algorithm has even a negligible influence on the data sampling process, so the results are not shown. It should be noted the GPR method is able to generate a comparably accurate PES with fewer data points than NNs 11,12,37,39 . However, training and evaluating the GPR-based PES become exponentially more expensive with the increasing number of points involved.…”

High-dimensional potential energy surfaces for molecular simulations: from empiricism to machine learning

“…Another challenge is to reduce the number of points required to define such a PES. Efforts in this direction have recently shown that with as few as 300 reference points the PES for scattering calculations in OH+H 2 can be described from a fit based on Gaussian processes together with Bayesian optimization [182]. Nevertheless, such high-accuracy representations of PESs for extended systems will remain a challenge for both, the number of high-quality reference calculations required and the type of inter-(and extra-)polation used to represent them.…”

Bayesian machine learning for quantum molecular dynamics

“…Rather, the purpose of reinforcement learning is to build a model that maps various input states onto desired outputs through an iterative process guided by some reward policy. An example of reinforcement learning is the inverse scattering problem aiming to construct a ML model of a potential energy surface that yields quantum dynamics results in full agreement with experimental results [23]. In the present article, most of the focus is on supervised and reinforcement learning, as well as optimization with machine learning.…”