A parallel adaptive method for pseudo-arclength continuation
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Bibliographic record
Abstract
We parallelize the pseudo-arclength continuation method for solving nonlinear systems\nof equations. Pseudo-arclength continuation is a predictor-corrector method where the\ncorrection step consists of solving a linear system of algebraic equations. Our algorithm\nparallelizes adaptive step-length selection and inexact prediction. Prior attempts to parallelize\npseudo-arclength continuation are typically based on parallelization of the linear\nsolver which leads to completely solver-dependent software. In contrast, our method is\ncompletely independent of the internal solver and therefore applicable to a large domain\nof problems. Our software is easy to use and does not require the user to have extensive\nprior experience with High Performance Computing; all the user needs to provide is the\nimplementation of the corrector step. When corrector steps are costly or continuation\ncurves are complicated, we observe up to sixty percent speed up with moderate numbers\nof processors. We present results for a synthetic problem and a problem in turbulence.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 it