Efficient determination of critical parameters of nonlinear\n Schr\\"{o}dinger equation with point-like potential using generalized\n polynomial chaos methods
Bibliographic record
Abstract
We consider the nonlinear Schr\\"{o}dinger equation with a point-like source\nterm. The soliton interaction with such a singular potential yields a critical\nsolution behavior. That is, for the given value of the potential strength and\nthe soliton amplitude, there exists a critical velocity of the initial soliton\nsolution, around which the solution is either trapped by or transmitted through\nthe potential. In this paper, we propose an efficient method for finding such a\ncritical velocity by using the generalized polynomial chaos method. For the\nproposed method, we assume that the soliton velocity is a random variable and\nexpand the solution in the random space using the orthogonal polynomials. The\nproposed method finds the critical velocity accurately with spectral\nconvergence. Thus the computational complexity is much reduced. Numerical\nresults for the smaller and higher values of the potential strength confirm the\nspectral convergence of the proposed method.\n
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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".