8. Problems Not Addressed in This Book
Bibliographic record
Abstract
Prediction is difficult, especially of the future. —Niels Bohr (1885–1962) It is not the goal of this tutorial to compile a complete compendium on partial differential equations (PDEs), solvers, and parallelization. Each section of this tutorial can still be extended by many, many more methods as well as by theory covering other types of PDEs. Depending on the concrete problem the following topics, not treated in the book, may be of interest: • Nonsymmetric problems, time-dependent PDEs, nonlinear PDEs, and coupled PDE problems [47, 103, 108]. • Error estimators and adaptive solvers [90, 109]. • Algorithms and programs that calculate the decomposition of nodes or elements to achieve a static load balancing, e.g., the programs Chaco [63], METIS [69], and JOSTLE [112]. See also [7, 74, 55] for basics and extensions of the techniques used. • Dynamic load balancing [9, 17]. • The wide range of domain decomposition (DD) algorithms. A good overview of research activities in this field can be found in the proceedings of the Domain Decomposition Conferences (see [42, 18, 19, 43, 70, 87, 72, 44, 10, 78, 76, 20]) and in the collection [71]. Two pioneering monographs give a good introduction to DD methods from two different points of view: the algebraic one [97] and the analytic one [88].
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.002 | 0.001 |
| 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".