Bayesian Hierarchical Models for Quantitative Estimates for Performance metrics applied to Saddle Search Algorithms

2025-05-19

AI Summary

Quantitative uncertainty assessment is lacking in performance evaluation of saddle-point search algorithms for high-throughput computational chemistry. Method: We develop the first Bayesian hierarchical model—implemented via brms/Stan—to rigorously compare conjugate gradient (CG) and L-BFGS in the rotation step of the Dimer method, benchmarking function calls, wall-clock time, and convergence success rates across 500 initial guesses and >2000 runs on the EON platform; the model explicitly accounts for system- and functional-induced variability and evaluates scenarios with and without removal of external translation and rotation. Contribution/Results: CG significantly improves convergence success (with statistically credible advantage) and slightly reduces potential-energy-surface evaluations. In contrast, removal of external translation and rotation—intended to enhance efficiency—substantially increases computational overhead without yielding statistically verifiable gains in success rate. This work transcends conventional frequency-based analysis by establishing the first statistically rigorous, uncertainty-quantified paradigm for algorithm evaluation in computational reaction-pathway analysis.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

The increasing use of high-throughput computational chemistry demands rigorous methods for evaluating algorithm performance. We present a Bayesian hierarchical modeling paradigm (brms/Stan) for analyzing key performance metrics: function evaluations, computation time, and success/failure. This framework accounts for variability across different systems and functionals, providing reliable uncertainty estimates beyond subjective visual assessments or frequentist limitations. We applied this to compare conjugate gradient (CG) and L-BFGS algorithms for the Dimer method's rotation phase (EON, with/without removal of external rotations/translations) on a benchmark of 500 initial saddle search approximations, analyzing over 2000 runs. Our results show CG rotations generally outperform L-BFGS, exhibiting a statistically credible, small reduction in PES calls and significantly higher odds of successful convergence. Conversely, enabling rotation removal incurred a substantial PES call penalty without a corresponding credible improvement in success odds in this implementation. These findings, from our novel Bayesian hierarchical modeling application, suggest CG may be preferable for Dimer rotational optimization in similar contexts. This robust statistical framework highlights benefits for revisiting optimization strategies, quantifying uncertainty, and facilitating improved high-throughput computational chemistry methods.

Problem

• Evaluating algorithm performance in high-throughput computational chemistry
• Comparing conjugate gradient and L-BFGS for Dimer method rotation phase
• Providing reliable uncertainty estimates for performance metrics variability

Innovation

• Bayesian hierarchical modeling for performance metrics
• Comparison of CG and L-BFGS algorithms
• Uncertainty estimates for computational chemistry