Optimization and Automation of the Construction of Smooth Free Energy Profiles
Bibliographic record
Abstract
An adaptive procedure is introduced to construct smooth analytical profiles of the free energy along a reaction coordinate using sampled data from multiple biased simulations. The procedure is based upon identifying problematic regions encountered in maximum likelihood estimators of the profile where there are statistically relevant discrepancies between the empirical and parametrized cumulative distribution functions and preferentially improving the construction of the parametric profile in these regions. The method is designed to produce continuous and smooth analytical fits that satisfy statistical goodness-of-fit tests with a minimum number of parameters. The accuracy of the profile obtained from the adaptive construction is compared by numerical computation to that of smooth interpolations based on an optimally chosen weighted histogram method for a solvated ion pair system and for an activated process for which the analytical form of the potential of mean force is available. In the model where the exact profile is known, the adaptive procedure is shown to reduce the integrated error relative to the optimal histogram construction by a factor of 3 or more in the typical case where the sampling is not extensive. It is demonstrated that the adaptive procedure can be used to produce statistically accurate smooth analytical representations of the free energy profile that can be evaluated with little computational effort and require little user input.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".