Fast Force Algorithms and Solar System Integrations
Bibliographic record
Abstract
Symplectic integrators have been the backbone of much theoretical solar system research over the past decade. As implemented, they involve the direct computation of the distances between each pair of N particles, a process whose effort grows as O(N2). A variety of fast [that is, with effort growing more slowly than O(N2)] but approximate force calculation methods have been developed in other areas of research. Several of these algorithms are examined here, and their speed and accuracy are compared with traditional methods, with an eye toward their suitability for solar system research in particular. We find that approximate force algorithms can provide, in some situations, a suitable alternative to traditional ones, with break-even in terms of computation time at particle numbers as low as a few hundred, and often with only modest increases in the short-term error. Though empirically stable on the systems tested here, the effect of approximate methods on the phase-space manifold of the problem remains a concern.
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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 | 0.000 | 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 | 0.000 |
| 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 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".