An Adaptive Sampling Procedure with Hyperreduction for Non-linear Petrov-Galerkin Reduced-Order Models
Bibliographic record
Abstract
Projection-based reduced order models (PROMs) have been shown in many applications to be accurate, reliable, and robust when approximating high-dimensional, differential equation-based computational models. For this reason, it has been proposed as a tool for high-querying parametric design problems like those arising in modern aircraft design. Since aerodynamic simulations can be computationally expensive, the PROMs should allow for more rapid estimations of high-fidelity solutions. However, the efficiency of PROMs can still be tied to the dimension of the full-order model (FOM), particularly when projected quantities must be frequently recomputed due to non-linearities or parameter dependence. In the case of Petrov-Galerkin models, the projected residual and Jacobian are re-evaluated at every Newton iteration, thus limiting the expected cost improvements. Hyperreduction is one of the tools available to approximate these quantities. In this paper, the energy-conserving sampling and weighting (ECSW) method will be tested as a possible approach for hyperreduction. It will be incorporated with previous work which had designed an adaptive sampling procedure for building a reduced-order model (ROM) with a controlled output error. The impacts on computational cost and accuracy will be studied for various test cases.
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How this classification was reachedexpand
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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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)
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 teacher head, 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".