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

2025-10-07

AI Summary

Gaussian process (GP)-based saddle-point search on high-dimensional potential energy surfaces suffers from low efficiency and poor robustness due to expensive hyperparameter optimization and insufficient model expressiveness. Method: We propose a physics-guided adaptive pruning strategy that integrates geometry-aware optimal transport theory. Specifically, we design an atom-type-weighted, permutation-invariant Wasserstein distance and introduce logarithmic barrier functions coupling trust radius with signal variance to balance model diversity preservation and update cost control. Active pruning, farthest-point sampling, and adaptive subset selection are innovatively embedded into the GP framework. Results: Evaluated on 238 chemical reaction pathways, our method reduces average computational time by over 50%, significantly enhancing the efficiency, stability, and scalability of GP-based saddle-point searches on complex potential energy surfaces.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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 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.

Problem

• Accelerating saddle point searches on high-dimensional energy surfaces
• Reducing computational overhead in hyperparameter optimization for Gaussian processes
• Enhancing robustness by preventing failures in underrepresented GP regions

Innovation

• Adaptive pruning reduces Gaussian process computational overhead
• Geometry-aware optimal transport ensures diverse configuration sampling
• Permutation-invariant metrics enhance stability with trust radius