Analysis of the effects and causes of numerical error in four-wave mixing simulations
Bibliographic record
Abstract
We present an investigation of accumulated numerical error in the simulation of four-wave mixing, which is frequently used to model a variety of nonlinear optical devices. The Dormand-Prince method (commonly used by commercial solving software such as MATLAB) has been found to be susceptible to numerical error, which manifests itself in a 3.8% increase in the total power over 200 m of nonlinear interaction length. This numerical error can lead to qualitatively mistaken physical interpretations of simulation results, which are similar to those found in previously published materials. We use a home-built Adams-Bashforth solver to simulate four-wave mixing, which produces results that do not lead to unphysical results, even for simulation over a large nonlinear interaction length. By comparing the results of these two methods we were able to illustrate the qualitative effects of the accumulated numerical error in the former. The source of this cumulative power error is traced to the solutions provided by the Dormand-Prince method for the self- and cross-phase modulation terms of the coupled mode equations; this error increases for larger nonlinearities or if step size increases. Even when this power accumulates from infinitesimal per-step errors, significant changes occur that could lead to qualitative differences in generated power values and conversion efficiencies. This reveals the potential danger of applying commonly used numerical solvers in simulating nonlinear optical processes.
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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 | 0.003 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".