Adaptive Pruning for Increased Robustness and Reduced Computational
  Overhead in Gaussian Process Accelerated Saddle Point Searches
Authors: name: Rohit Goswami, name: Hannes Jónsson

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 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.