Evaluating the Risk of Local Optima in Aerodynamic Shape Optimization
Bibliographic record
Abstract
A gradient-based multistart method based on a set of 17 to 33 random initial geometries is used to examine the risk associated with multimodality when applying gradient-based optimization to aerodynamic shape optimization. Aerodynamic shape optimization problems typical of detailed, preliminary, and exploratory design are shown to consistently present design spaces with multiple local optima. In the case of detailed design, the risk of converging to a local optimum with performance significantly inferior to that of the best local optimum found is reduced due to the ability of a well-designed initial geometry, which is often available for such problems, to converge to a well-performing local optimum. In problems permitting increased geometric freedom typical of preliminary design, the risk associated with multimodality is much higher. This risk is further exacerbated in exploratory cases where high geometric freedom is combined with limited knowledge of the design space in question and hence greater differences between available initial geometries and the optimal geometry. Therefore, for preliminary and exploratory design, allocating resources toward addressing multimodality can significantly reduce the risk of overlooking a superior optimum.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.007 | 0.024 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".