Moving least-squares enhanced Shepard interpolation for the fast marching and string methods
Bibliographic record
Abstract
The number of the potential energy calculations required by the quadratic string method (QSM), and the fast marching method (FMM) is significantly reduced by using Shepard interpolation, with a moving least squares to fit the higher-order derivatives of the potential. The derivatives of the potential are fitted up to fifth order. With an error estimate for the interpolated values, this moving least squares enhanced Shepard interpolation scheme drastically reduces the number of potential energy calculations in FMM, often by up 80%. Fitting up through the highest order tested here (fifth order) gave the best results for all grid spacings. For QSM, using enhanced Shepard interpolation gave slightly better results than using the usual second order approximate, damped Broyden-Fletcher-Goldfarb-Shanno updated Hessian to approximate the surface. To test these methods we examined two analytic potentials, the rotational dihedral potential of alanine dipeptide and the S(N)2 reaction of methyl chloride with fluoride.
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".