A Rational Approach to Curve Representation
Why this work is in the frame
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Bibliographic record
Abstract
This paper introduces an approach to construct a rational function that fits the finite set of data points on the B-H plane representing the non-linear response of a permeable material, providing an approximation to the data well-suited for interpolation and extrapolation. Improving on previous methods, this approach provides a smooth, closed-form approximation to the data capable of representing the material's response from its Rayleigh region through to its saturation, appropriate for use with finite-element solvers. This is achieved by applying the method of vector fitting (as seen in the discipline of control systems) to the B-H data set, while taking care to remove pole-zero pairs that may occur between data points. The method is demonstrated to provide high-accuracy approximations to the data sets of a range of materials. Good agreement with measured data is obtained when the rational material representation is used in a finite-element software package to solve the TEAM 13 benchmark problem. A rational function expression for the TEAM 13 permeability is provided.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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 | 0.001 |
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 it