Automatic numerical solver selection from a repository of pre-run simulations
Bibliographic record
Abstract
Numerical solver uncertainty is high when the solutions of the differential equations of a model, computed with different numerical solvers, deviate from each other. Numerical solver uncertainty is a serious limiting factor of the simulation process and can lead to incorrect model predictions. This problem is especially critical because the correct solution trajectory of environmental models, often consisting of large systems of ODEs, is almost always unknown. The selection of the most appropriate solver, according to speed and correctness, is not a straightforward task and cannot be based on, for instance, literature. Moreover, with the advent of distributed computing, large amounts of data on previously run simulations are readily available. Analyzing these data can help automating the selection of the most appropriate solver. A new methodology for this automatic selection, based on the correctness of the solution from a repository of simulations, was developed and tested on a set of 16 models with different levels of complexity. This methodology is capable of finding deviating solutions when the model is computed with different solvers and settings, and shows that numerical solver uncertainty is quite common. A cluster of appropriate solvers, which are able to solve the model correctly, can be identified and the most efficient solver can be selected among them. This results in a reduction of the numerical solver uncertainty. On top of that, it was also possible to achieve a reduction of the computation time by a factor of 10(6), compared to slow, but undoubtedly correct solvers.
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How this classification was reachedexpand
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".