Efficient Hyperreduction by Empirical Quadrature Procedure with Constraint Reduction for Large-scale Parameterized Nonlinear Problems
Bibliographic record
Abstract
Many engineering applications require rapid and reliable approximations of parameterized nonlinear partial differential equations. Model order reduction (MOR) constructs a low-dimensional model in the offline stage such that we can rapidly calculate outputs for any parameter value in the online stage. For equations with general nonlinearities, MOR requires hyperreduction, which can be computationally expensive. In this work, we improve the offline-efficiency of empirical quadrature procedure (EQP) used for hyperreduction. EQP involves solving a constrained minimization problem, often with a large set of constraints. We propose four modifications to EQP. First, we consider second-order error contributions to achieve smaller error tolerances. Second, we propose a rounding-error stable constraint residual calculation method, reducing offline cost. Third, and most importantly, we develop a constraint reduction method, employing QR factorization to reduce the number of constraints and thus improve offline-efficiency. Fourth, we develop an efficient sampling procedure for problems with high-dimensional parameter spaces.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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".