Truncated-Newton Method with Adjoint-based Hessian-vector Product for Aerodynamic Shape Optimization Problems
Bibliographic record
Abstract
Computational fluid dynamics with numerical optimization has been a dominant design method in aerospace engineering. Newton’s method is a widely-used optimization approach which converges rapidly. In each iteration of the Newton framework, a Hessian matrix needs to be formulated and a linear system is solved to acquire the search direction. The evaluation of an accurate Hessian brings considerable numerical cost. Therefore, the current work proposes a truncated-Newton method with a Hessian-vector product approach. The formulation of the Hessian-vector product is derived based on an adjoint-adjoint approach. A twisted Conjugate-gradient method is adopted to solve the linear system of the Newton’s method. The Hessian-vector product is embedded in the Conjugate-gradient method to compute an inaccurate solution to the linear system. It is shown that by only solving the linear system for a few iterations, the numerical cost is greatly reduced while the solution still provides a sufficient descent direction. The effect of different convergence levels on the performance of aerodynamic optimization is studied and compared with previous work for a quasi-one-dimensional test case. A three-dimensional inviscid aircraft wing test case is used to demonstrate the effectiveness of the method.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| 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) | 0.004 | 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".