Truncated-Newton Method with Adjoint-based Hessian-vector Product for Aerodynamic Shape Optimization Problems
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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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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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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 it