Least-squares reconstruction of a 3D potential from its measured spatial velocity field
Bibliographic record
Abstract
This paper describes a new method for the least-squares reconstruction of a hypersurface from measured 3D gradient data, for example, the potential function of a measured velocity field. The novel aspect of the proposed algorithm is that the solution relies on representing 3D data with hypermatrices, and obtaining the least-squares solution to the problem as the solution of a hypermatrix equation, i.e., a set of linear equations that equates hypermatrices. The new approach enables the solution of the reconstruction problem over an l x m x n hypersurface in O(n^4) time (with l ~ m ~ n), whereas a straightforward approach of solving the problem with a standard least-squares approach (vectorization) would yield an order O(n^9) algorithm. The new algorithm is therefore five orders of magnitude faster than the state-of-the-art. The new algorithm is tested with synthetic data with synthetic noise. The method is, however, applicable to the problem of reconstructing a potential from velocity data measured, for example, via particle image velocimetry.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.019 | 0.003 |
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; both teacher heads agree on what is shown here.
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".