What is it about?
Saddle-search papers still rank methods by a mean wall time or a mean force-call count on a small test set. That mean hides system-to-system spread, so a ranking can be noise from the sample rather than a property of the algorithms. We fit Bayesian generalized linear mixed models, through brms and Stan, to dimer-method variants on 500 starting configurations near saddles (the Hermes set), with eOn and NWChem at Hartree-Fock / 3-21G. Each system is a random intercept. The models cover potential-energy-surface (PES) call counts, wall time, and binary success. Conjugate-gradient rotation has a small PES-call advantage over L-BFGS (median 2.6 percent more calls for L-BFGS, 95 percent credible interval 0.7 to 4.5 percent) and much higher odds of success (L-BFGS odds ratio 0.3, interval 0.13 to 0.60). Turning on external-rotation removal costs a median 44.2 percent more PES calls (41.6 to 46.8 percent) and does not raise success in the full model.
Featured Image
Photo by Dan Cristian Pădureț on Unsplash
Why is it important?
A table of means cannot say whether conjugate gradient is more reliable than L-BFGS or whether a few hard molecules moved the average. The hierarchical posterior reports a credible interval on the effect and a between-system variance. That is what a high-throughput workflow needs before it picks a default. The same model structure is not tied to dimers. Any benchmark that repeats algorithms across test problems can reuse it. The paper therefore argues for a chain of methods: try conjugate gradient without rotation removal first, and fall back to rotation removal only on the systems that fail.
Perspectives
I was ranking dimer variants for the thesis and the means would not sit still. Change the test set and the winner moved. Some methods were fast on easy molecules and died on hard ones. Averages hid that. Hierarchical models in brms were the tool that matched the data: runs nested in systems, a random intercept for each molecule, and a full posterior on the contrast. The 44 percent PES-call penalty for rotation removal, with no credible success gain in the full model, is the number that changed how I run a default search. The repository pins eOn, NWChem, and the R analysis so the ranking can be rebuilt.
Rohit Goswami
University of Iceland
Read the Original
This page is a summary of: Bayesian hierarchical models for quantitative estimates for performance metrics applied to saddle search algorithms, AIP Advances, August 2025, American Institute of Physics,
DOI: 10.1063/5.0283639.
You can read the full text:
Resources
Contributors
The following have contributed to this page
