A local Gaussian Processes method for fittingpotential surfaces that obviates the need to invertlarge matrices
Bibliographic record
Abstract
In order to compute a vibrational spectrum, one often wishes to start with a set of ab initio Born-Oppenheimer potential values at points, called fitting points, and interpolate or fit to find values of the potential at quadrature or collocation points. It is common to do this once to build a potential energy surface (PES). Once the PES is known, it can be evaluated at any point in configuration space. Gaussian Process (GP) is frequently being used to make a PES. As is the case in other interpolation methods, to use GP one must store and invert a matrix whose size is the number of fitting points. The matrix is sometimes large enough that approximations are introduced to reduce the cost of the calculation. We show that is possible to use many local Gaussian Process fits rather than one global fit. Retaining only local Gaussians and the associated points works well despite the fact that other Gaussians have tails with significant amplitude in the local region. We demonstrate that from the potential values obtained from the local fits it is possible to compute accurate energy levels of formaldehyde. In one calculation, potential values were obtained with N = 120, 000 fitting points by inverting matrices of size less than m = 400. The local idea reduces the cost from N^3 to T(m3 + N), where T is the number of desired potential points.
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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 | 0.001 | 0.003 |
| 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 | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.013 | 0.005 |
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".