Sensitivity-Based Sequential Sampling of Cokriging Response Surfaces for Aerodynamic Data
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Bibliographic record
Abstract
Modern aircraft design involves a large number of parameters, and obtaining flow solutions for all combinations of such parameters is not realistically feasible. Aerodynamicists can therefore only afford a limited number of flow solutions, and they often rely on surrogate models to reconstruct the continuous response surface of the system. This work is focused on surrogate models of the Kriging family, especially the gradient enhanced version called Cokriging. One challenge in constructing Cokriging response surfaces is the selection of input parameters locations in the design space. This process called sampling is often conducted in an iterative manner, through successive response surface refinements involving error analysis at each step. Appropriate error analysis is key to efficient sampling. In this article, a new error estimate for Cokriging response surfaces using readily available gradient information is introduced and tested in a sampling context on analytical and real aerodynamic cases. Nomenclature N = number of snapshots Nsnap = number of snapshots Noutput = number of points on output response surface D = dimension of design space / number of parameters P = order of regression polynomial Dbasis = dimension of regression polynomial basis x = position vector [1xD] in the design space x = position vectors tensor [NsnapxD] y(x) = value of the objective function at x ŷ(x) = Kriging approximation of y(x) / response surface value at x R = correlation matrix [NsnapxNsnap] r = correlation vector [1xNsnap] f = regression vector [1xDbasis] F = regression matrix [NsnapxDbasis] i = snapshot index j = output response surface point index J = jacobian matrix [NoutputxNsnap] S = sensitivity matrix [NoutputxNsnap] S = sensitivity vector [Noutputx1] ∗Undergraduate Student, Computational Aerodynamics Group, McGill University. MacDonald Eng. Build., Room 256. arthur.paul-dubois-taine@mail.mcgill.ca Phone: 514 746 2704 †Associate Professor, Computational Aerodynamics Group, McGill University. MacDonald Eng. Build., Room 159 1 of 19 American Institute of Aeronautics and Astronautics
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.001 |
| 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