GUDERMANNIAN NEURAL NETWORKS TO INVESTIGATE THE LIÉNARD DIFFERENTIAL MODEL
Bibliographic record
Abstract
The aim of this study is to present the numerical solutions of the Liénard nonlinear model by designing the structure of the computational Gudermannian neural networks (GNNs) along with the global/local search efficiencies of genetic algorithms (GAs) and interior-point algorithm (IPA), i.e. GNNs–GAs–IPA. A merit function in terms of differential system and its boundary conditions is designed and optimization is performed by using the proposed computational procedures of GAs–IPA to solve the Liénard nonlinear differential system. Three different highly nonlinear examples based on the Liénard differential system have been tested to check the competence, exactness and proficiency of the proposed computational paradigm of GNNs–GAs–IPA. The statistical performances in terms of different operators have been provided to check the reliability, consistency and stability of the computational GNNs–GAs–IPA. The plots of the absolute error, performance measures, results comparison, convergence analysis based on different operators, histograms and boxplots are also illustrated. Moreover, statistical gauges using minimum, mean, maximum, semi-interquartile range, standard deviation and median are also provided to authenticate the optimal performance of the GNNs–GAs–IPA.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".