Error Sampling and Synthesis for High-Order Node Movement
Bibliographic record
Abstract
The presented work focuses on the error sampling and synthesis procedure within an optimization framework for high-order, metric-based mesh adaptation in high-order, finite-element (FEM) discretization. This mesh optimization framework is designed to handle arbitrary FEM discretization order, geometry order, and element types. In performing a metric-based adaptation, the framework uses a high-order Riemannian metric field to encode the curvature, anisotropy, and global coupling between vertices and high-order geometry nodes. An error model and a cost model are employed to iteratively construct the desired Riemannian metric field and guide a series of globally coupled vertex (r-adaptation) and high-order geometry (q-adaptation) node movements. The resulting mesh is an optimal high-order (curved) mesh that conforms to the specified metric field. The error model requires an error sampling and synthesis procedure, which involves several steps, including element splitting, random sampling of high-order geometry node movements, and estimating the metric-based error kernel on each mesh element. This paper aims to: 1) discuss the theoretical underpinnings of a robust, a posteriori, metric-based error model for qr-adaptation and 2) provide a status update on the 1D HOMES algorithm, which is a native extension of the Mesh Optimization via Error Sampling and Synthesis (MOESS) algorithm to a higher order.
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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 | 0.002 | 0.006 |
| 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".