An online-adaptive hyperreduced reduced basis element method for parameterized component-based nonlinear systems using hierarchical error estimation
Bibliographic record
Abstract
We present an online-adaptive hyperreduced reduced basis element method for model order reduction of parameterized, component-based nonlinear systems. The method, in the offline phase, prepares a library of hyperreduced archetype components of various fidelity levels and, in the online phase, assembles the target system using instantiated components whose fidelity is adaptively selected to satisfy a user-prescribed system-level error tolerance. To achieve this, we introduce a hierarchical error estimation framework that compares solutions at successive fidelity levels and drives a local refinement strategy based on component-wise error indicators. We also provide an efficient estimator for the system-level error to ensure that the adaptive strategy meets the desired accuracy. Component-wise hyperreduction is performed using an empirical quadrature procedure, with the training accuracy guided by the Brezzi–Rappaz–Raviart theorem. The proposed method is demonstrated on a family of nonlinear thermal fin systems comprising up to 225 components and 68 parameters. Numerical results show that the hyperreduced reduced basis element model achieves computational reduction at 1% error level relative to the truth finite-element model. In addition, the adaptive refinement strategy provides more effective error control than uniform refinement by selectively enriching components with higher local errors.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".