Optimal transport for particle image velocimetry
Bibliographic record
Abstract
We present a new method for particle image velocimetry, a technique using successive laser images of particles immersed in a fluid to measure the velocity field of the fluid flow. The main idea is to recover this velocity field via the solution of the L 2 -optimal transport problem associated with each pair of successive distributions of tracers. We model the tracers by a network of Gaussian-like distributions and derive rigorous bounds on the approximation error in terms of the model's parameters. To obtain the numerical solution, we employ Newton's method, combined with an efficient spectral method, to solve the Monge-Ampre equation associated with the transport problem. We present numerical experiments based on two synthetic flow fields, a plane shear and an array of vortices. Although the theoretical results are derived for the case of a single particle in dimensions one and two, the results are valid in R d , d 1. Moreover, the numerical experiments demonstrate that these results hold for the case of multiple particles, provided the Monge-Ampre equation is solved on a fine enough grid.
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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 | 0.002 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.003 | 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".