Parallel Multigrid Acceleration for the Finite-Element Gaussian Belief Propagation Algorithm
Bibliographic record
Abstract
We introduce a novel parallel multigrid algorithm, referred to as the finite-element multigrid Gaussian belief propagation (FMGaBP), to accelerate the convergence of the recently introduced finite-element Gaussian belief propagation solver. The FMGaBP algorithm processes the FEM computation in a fully distributed and parallel manner, with stencil-like element-by-element operations, demonstrating high parallel efficiency. The results for both sequential as well as parallel message scheduling versions of FMGaBP demonstrate high convergence rates independent of the scale of discretization on the finest mesh. In comparison with the multigrid preconditioned conjugate gradient (MG-PCG) solver, the FMGaBP algorithm demonstrates considerable iteration reductions as tested by Laplace benchmark problems. In addition, the parallel implementation of FMGaBP shows a speedup of 2.9 times over the parallel implementation of MG-PCG using eight CPU cores.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".