Shape Optimization Under a Constraint on the Worst-Case Scenario
Bibliographic record
Abstract
Abstract. This work falls within the general framework of robust shape optimization under constraints, where a physical parameter of the problem is poorly known. In particular, we study problems where one of the constraints concerns the maximal possible value that a given shape functional can assume when the uncertain parameter varies within an admissible range. Two different approaches are considered: the first one based on the approximation of the set of admissible uncertain parameters by a convex polyhedron, and the second one relying on the notion of subdifferential in the sense of Clarke. The main contributions of this work consist in the theoretical proof of convergence of the first approach under suitable hypotheses of convexity of the set of admissible parameters and of the constraint, and the adaptation of Clarke’s subdifferential in the context of robust shape optimization. The two techniques are compared numerically in three examples, with the objective of minimizing the volume of elastic structures under a constraint on the worst-case scenario for the mechanical compliance and the von Mises stress.
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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 | 0.001 | 0.007 |
| 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 | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.010 | 0.001 |
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".