Hessian Matrix Update Scheme for Transition State Search Based on Gaussian Process Regression
Alexander Denzel, Johannes Kästner
Abstract
We show how Gaussian process regression can be used to update Hessian matrices using gradient-based information in the course of an optimization procedure. This is done by building a Gaussian process with at least one initial Hessian and some further energies and gradients from electronic structure calculations and evaluating the desired second derivative of the resulting Gaussian process. To a certain extent, we can overcome the significant scaling problems that occur when training a Gaussian process with Hessian information. We demonstrate in benchmark runs using the partitioned rational function optimization (P-RFO) that this new update method can outperform classical Hessian update methods for small systems.