# Adaptive Pruning for Increased Robustness and Reduced Computational Overhead in Gaussian Process Accelerated Saddle Point Searches

## TL;DR

This paper introduces a new method to speed up and stabilize complex energy calculations using Gaussian processes with adaptive pruning and optimal transport.

## Contribution

A novel adaptive pruning strategy using Wasserstein distances and optimal transport improves robustness and efficiency in Gaussian process-based saddle point searches.

## Key findings

- The new method reduces mean computational time by over 50% on a dataset of 238 chemical reaction configurations.
- Geometry-aware optimal transport measures enhance stability and prevent failures in unrepresented regions of the energy surface.
- A permutation-invariant metric with logarithmic barrier penalty ensures reliable early stopping and trust radius estimation.

## Abstract

Gaussian process (GP) regression provides a strategy for accelerating saddle point searches on high‐dimensional energy surfaces by reducing the number of times the energy and its derivatives with respect to atomic coordinates need to be evaluated. The computational overhead in the hyperparameter optimization can, however, be large and make the approach inefficient. Failures can also occur if the search ventures too far into regions that are not represented well enough by the GP model. Here, these challenges are resolved by using geometry‐aware optimal transport measures and an active pruning strategy using a summation over Wasserstein‐1 distances for each atom‐type in farthest‐point sampling, selecting a fixed‐size subset of geometrically diverse configurations to avoid rapidly increasing cost of GP updates as more observations are made. Stability is enhanced by a permutation‐invariant metric that provides a reliable trust radius for early‐stopping and a logarithmic barrier penalty for the growth of the signal variance. These physically motivated algorithmic changes prove their efficacy by reducing to less than a half the mean computational time on a set of 238 challenging configurations from a previously published data set of chemical reactions. With these improvements, the GP approach is established as a robust and scalable algorithm for accelerating saddle point searches when the evaluation of the energy and atomic forces requires significant computational effort.

Optimal Transport: A permutation‐invariant "harness" measures true geometric distance improves performance and robustness.© 2026 WILEY‐VCH GmbH