Gaussian Process Regression for Geometry Optimization

TL;DR

This paper introduces a Gaussian process regression-based geometry optimizer that outperforms traditional methods in reducing optimization steps by effectively modeling potential energy surfaces.

Contribution

The paper presents a novel GPR-based optimizer with a detailed methodology and demonstrates its superior performance over L-BFGS in benchmark tests.

Findings

Matérn kernel outperforms squared exponential kernel

GPR optimizer reduces number of optimization steps

Effective overshooting improves interpolation accuracy

Abstract

We implemented a geometry optimizer based on Gaussian process regression (GPR) to find minimum structures on potential energy surfaces. We tested both a two times differentiable form of the Mat\'{e}rn kernel and the squared exponential kernel. The Mat\'{e}rn kernel performs much better. We give a detailed description of the optimization procedures. These include overshooting the step resulting from GPR in order to obtain a higher degree of interpolation vs. extrapolation. In a benchmark against the L-BFGS optimizer of the DL-FIND library on 26 test systems, we found the new optimizer to generally reduce the number of required optimization steps.