Matching a Given Field Using Hierarchal Vector Basis Functions
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Bibliographic record
Abstract
Unlike interpolatory finite elements, hierarchal elements offer no straightforward way to approximate a given field. The vector case in particular is challenging. A solution is proposed which, though developed for a specific series of tetrahedral vector elements, is applicable to other noninterpolatory elements. The method uses a projective, rather than a point-matching, approach, for greater accuracy. It avoids the inversion of a large matrix and employs precomputed (universal) matrices wherever possible for efficiency. By considering explicitly the matching of the curl of the field as well as the field itself, it is able to maintain the asymptotic error performance associated with the use of common “mixed order” elements, such as the Whitney edge element. The error performance is demonstrated by a test case involving the dominant mode of rectangular waveguide.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it