Geometry-aware data pruning halves wall time for GP-accelerated saddle searches

What is it about?

Gaussian process (GP) regression can accelerate saddle point searches by building a surrogate energy surface on the fly, reducing the number of expensive quantum mechanical force evaluations. But as the GP collects data during a search, the cost of updating the model grows cubically with dataset size. On large problems, the surrogate model itself becomes the bottleneck. We solve this with farthest-point sampling guided by the Earth Mover's Distance, a metric that measures structural similarity between molecular configurations in a permutation-invariant way. At each step, only a compact subset of geometrically diverse configurations feeds the hyperparameter optimization, while all data remain available for predictions. The cost of model updates stays nearly constant regardless of how many data points have been collected. Three stability controls complement the pruning: a logarithmic barrier on the signal variance, an oscillation detector that expands the training subset when the optimizer becomes unstable, and a data-driven trust radius based on the same transport distance. On a benchmark of 238 molecular reactions, the method (OT-GP) halves the mean wall time relative to its predecessor, requires a median of fewer than 30 force evaluations, and raises the success rate from 86% to 96%.

Featured Image

Why is it important?

Previous GP-accelerated saddle searches reduced force evaluation counts by an order of magnitude but often failed to deliver practical wall-time improvements because the hyperparameter optimization overhead grew with every new observation. The model also suffered from instabilities -- diverging variance, oscillating hyperparameters -- that caused silent failures on difficult systems. OT-GP addresses both problems through the same geometric framework. The optimal transport metric provides a physically motivated measure for data selection (pruning) and for determining when the model can be trusted (trust radius). The stability controls were each designed to address a specific failure mode diagnosed on real chemical systems. The combination of 2x wall-time reduction, 96% success rate, and fewer than 30 median force evaluations makes automated exploration of reaction networks practical at the DFT level. The method also provides training data for machine-learned interatomic potentials, since it generates exactly the high-energy transition state geometries that are underrepresented in typical training sets.

Perspectives