Application of physics-constrained data-driven reduced-order models to shape optimization
Bibliographic record
Abstract
This study proposes a novel approach for building surrogate models, in the form of reduced-order models(ROMs), for partial differential equation constrained optimization. A physics-constrained data-driven framework is developed to transform large-scale nonlinear optimization problems into ROM-constrained optimization problems. Unlike conventional methods, which suffer from instability of the forward sensitivity function, the proposed approach maps optimization problems to system dynamics optimization problems in Hilbert space to improve stability, reduce memory requirements, and lower computational cost. The utility of this approach is demonstrated for aerodynamic optimization of an NACA 0012 airfoil at $Re = 1000$ . A drag reduction of 9.35 % is obtained at an effective angle of attack of eight degrees, with negligible impact on lift. Similarly, a drag reduction of 20 % is obtained for fully separated flow at an angle of attack of $25^{\circ }$ . Results from these two optimization problems also reveal relationships between optimization in physical space and optimization of dynamical behaviours in Hilbert space.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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".