Modeling Error in L<sup>1</sup>for a Hierarchy of 1-D Discrete Velocity Models
Bibliographic record
Abstract
Abstract We consider the spatial difference in L 1 between solutions to two different discrete velocity models in one space dimension. We assume that the second (fine) model is obtained by adding new velocities to the first (coarse) model, although the collision operators can be completely different. The 1-D discrete velocity models studied here include projections of n-D models, as described by Beale. This work adapts the nonlinear and decreasing interaction functional of Ha and Tzavaras for discrete velocity models in 1-D in order to measure the distance in L 1 . The resulting functional increases by a term proportional to the residual of the modeling error for the coarse model. The modeling error can therefore be computed a posteriori and can be used to determine which discrete velocity model within a hierarchy satisfies a prescribed accuracy. Keywords: A posterioriBoltzmann equationDiscrete velocity modelError estimateModeling errorNonlinear hyperbolic equation. Supported by the Natural Sciences and Engineering Research Council of Canada and the Canadian Foundation for Innovation.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".