Structure-Preserving Integration Algorithms
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract. Often in physics and engineering one encounters systems of dierential equations that have a non-trivial dynamic or kinematic structure, e.g., the flow generated by such a system may satisfy one or more algebraic or dierential constraints. Moreover, this structure is often of physical signi cance, embodying an important concept such as conservation of energy. Traditional numerical methods for solving initial value problems typically do not preserve any structure possessed by the system and can be computationally less ecient than algorithms specically designed to honour a system’s structure. Also of interest are \\near ideal " systems, where some conservation property is only weakly violated. Through a series of examples drawn from various physical systems, we discuss numerical algorithms which, in each case, are specically constructed to preserve the structure of the system under consideration. These methods are shown to be of particular interest when the integration interval is signicantly longer than the characteristic time scale(s) of the system.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.018 | 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