Hierarchical Gaussian Process Regression for Meta-Learning of Molecular Geometry Optimization

Abstract

Quantum chemistry uses quantum mechanics for the first-principle exploration of chemical systems. In principle, all chemical phenomena can be studied by solving the Schrödinger equation, the approximate solutions of which, in practice, are computationally very expensive to find. From the approximate solutions of the many-electron Schrödinger equation, we can construct the potential-energy surfaces (PESs) – a fundamental concept used in chemistry.  

A PES is a multi-dimensional function that maps a given molecular geometry to electronic-structure energy. Characterizing the PES, a problem known as geometry optimization, is important as correctly identifying the local minima and saddle points of a PES can be applied to predict how fast a reaction occurs and provide atomistic-level insights.

Given the recent success of machine learning in solving computational tasks previously thought unsolvable, we propose to develop methods that apply Bayesian learning to perform meta-learning to speed up and scale geometry optimization of molecular PESs for main-group molecules. The idea of meta-learning is that experience from optimizing different molecules can be adapted to novel molecular systems and, consequently, be used to speed up the optimization of those systems. Reliable and efficient structural determination is the cornerstone for constructing comprehensive mechanistic analysis for large-scale atmospheric and materials modelings.