Gradient-Enhanced Bayesian Optimization With Application to Aerodynamic Shape Optimization
Bibliographic record
Abstract
Bayesian optimizers have several desirable properties that make them well suited for various aerodynamic shape optimization applications. For example, the design space can often be multimodal, and Bayesian optimizers are efficient global optimizers. Bayesian optimizers also enable the use of mixed-fidelity data, the use of inexact function and gradient evaluations, and uncertainty quantification thanks to their use of probabilistic surrogates. The challenges of applying a Bayesian optimizer to aerodynamic shape optimization problems include the high-dimensional design space, the nonlinear constraints, and their limited application to local optimization. A local optimization framework for a gradient-enhanced Bayesian optimizer is developed in this paper that is shown to be competitive with the popular quasi-Newton based optimizer SNOPT for the nonlinearly constrained aerodynamic shape optimization of a transonic airfoil. A recently developed preconditioning method is used to address the ill-conditioning of the gradient-enhanced covariance matrix, which enables the Bayesian optimizer to converge the optimality as deeply as SNOPT. With these developments, gradient-enhanced Bayesian optimization represents a versatile option for a wide range of challenging aerodynamic shape optimization problems, including unimodal and multimodal problems, and chaotic flows where calculating accurate gradients is challenging.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".