Active Learning for Saddle Point Calculation

TL;DR

This paper introduces an active learning framework combining Gaussian process regression and gentle accent dynamics to efficiently locate saddle points in energy landscapes, reducing costly gradient evaluations in computational chemistry.

Contribution

It proposes a novel active learning approach with an optimal experimental design criterion for saddle point calculation, improving efficiency over traditional methods.

Findings

Significantly reduces the number of energy and force evaluations needed.

Demonstrates improved efficiency in saddle point detection.

Employs a surrogate model to guide the search process.

Abstract

The saddle point (SP) calculation is a grand challenge for computationally intensive energy function in computational chemistry area, where the saddle point may represent the transition state (TS). The traditional methods need to evaluate the gradients of the energy function at a very large number of locations. To reduce the number of expensive computations of the true gradients, we propose an active learning framework consisting of a statistical surrogate model, Gaussian process regression (GPR) for the energy function, and a single-walker dynamics method, gentle accent dynamics (GAD), for the saddle-type transition states. SP is detected by the GAD applied to the GPR surrogate for the gradient vector and the Hessian matrix. Our key ingredient for efficiency improvements is an active learning method which sequentially designs the most informative locations and takes evaluations of the original model at these locations to train GPR. We formulate this active learning task as the optimal experimental design problem and propose a very efficient sample-based sub-optimal criterion to construct the optimal locations. We show that the new method significantly decreases the required number of energy or force evaluations of the original model.