Balancing parallel adaptive FEM computations by solving systems of linear equations
Bibliographic record
Abstract
Abstract. Load balancing plays an important role in parallel numerical simulations. State-of-the-art libraries addressing this problem base on vertex exchange heuristics that are embedded in a multilevel scheme. However, these are hard to parallelize due to their sequential nature. Furthermore, libraries like Metis and Jostle focus on a small edge-cut and cannot obey constraints like connectivity and straight partition boundaries, which are important for some numerical solvers. In this paper we present an alternative approach to balance the load in parallel adaptive finite element simulations. We compute a distribution that is based on solutions of linear equations. Integrated into a learning framework, we obtain a heuristic that contains a high degree of parallelism and computes well shaped connected partitions. Furthermore, our experiments indicate that we can find solutions that are comparable to those of the two state-of-the-art libraries Metis and Jostle also regarding the classic metrics like edge-cut and boundary length.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 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) | 0.007 | 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".