Effective filtering and interpolation of 2D discrete velocity fields with Navier–Stokes equations
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Bibliographic record
Abstract
We introduce a new variational technique to interpolate and filter a twodimensional velocity vector field which is discretely sampled in a region of 2 and sampled only once at a time, on a small time-interval DtThe main idea is to find a solution of the Navier-Stokes equations that is closest to a prescribed field in the sense that it minimizes the l 2 norm of the difference between this solution and the target field.The minimization is performed on the initial vorticity by expanding it into radial basis functions of Gaussian type, with a fixed size expressed by a parameter ò.In addition, a penalty term with parameter k e is added to the minimizing functional in order to select a solution with a small kinetic energy.This additional term makes the minimizing functional strongly convex, and therefore ensures that the minimization problem is well-posed.The interplay between the parameters k e and ò effectively contributes to smoothing the discrete velocity field, as demonstrated by the numerical experiments on synthetic and real data.
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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