A novel predictive homotopic path tracking algorithm to solve non‐linear algebraic equations
Why this work is in the frame
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Bibliographic record
Abstract
Abstract In chemical engineering and other areas of mathematics and engineering sciences, systems of non‐linear algebraic equations often must be solved, and a problem is that these types of systems often cannot be solved analytically. Homotopic continuation methods are globally convergent and can find several solutions to the analyzed algebraic system and consist of a predictive step followed by a corrective step, which can cause reversion of homotopic path tracking. Therefore, in this work, the use of a homotopy continuation method (HCM) based on a purely predictive methodology is proposed; that is, it only makes use of predictor vectors (without correction vectors) to find the solution to several systems of non‐linear algebraic equations with a multiplicity of solutions, employing lower central proccessing unit (CPU) time in comparison with standard homotopic tracking algorithms.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 it