A goal-oriented adaptive sampling procedure for projection-based reduced-order models with hyperreduction
Bibliographic record
Abstract
Projection-based reduced-order models (PROMs) are an invaluable tool for efficiently generating approximate solutions to high-dimensional, differential equation-based computational models across many applications. In the field of modern aircraft design, they are used to substitute costly computational fluid dynamics (CFD) simulations. This work builds on a previously developed goal-oriented adaptive sampling procedure that uses adjoint-based dual-weighted residual (DWR) error indicators to guide snapshot selection. This ensures the construction of an efficient PROM in addition to providing a way to estimate the expected error introduced in the functional of interest. The key contribution of this work is the integration of hyperreduction into this goal-oriented framework—both in the ROM solution process and in the DWR error estimation. This allows the construction of a hyperreduced-order model (HROM), through the use of the energy-conserving sampling and weighting (ECSW) method, that achieves the same functional error tolerance as a standard ROM, but at a significantly lower computational cost. The approach is demonstrated on a NACA 0012 airfoil with various problem configurations. The results indicate that despite the increased basis size needed to offset the additional error introduced by hyperreduction, the updated procedure enables efficient offline HROM construction and accurate online predictions. The results in this paper are limited to steady-state CFD problems, but the approach can be extended to unsteady CFD problems and other engineering problems of interest.
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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) | 0.002 | 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".