Accurate and efficient sensitivity analysis using the beam propagation method
Bibliographic record
Abstract
We discuss a novel technique for accurately estimating the sensitivities of any desired response based on the finite difference Beam Propagation Method (BPM). Our technique utilizes the central adjoint variable method (CAVM) for estimating the response sensitivities. Using only one simulation of the photonic structure, the response and its sensitivities with respect to all the design parameters are obtained regardless of their number. This approach features accuracy comparable to that of the central finite difference approximation applied at the response level. The effectiveness of our approach is illustrated by using different response functions and different structures. Our approach utilizes virtual perturbations of the system matrices. Central difference scheme is utilized to calculate the sensitivity of these matrices with respect to the designable parameters. This sensitivity is then utilized to efficiently estimate the sensitivity of the objective function. This technique has been applied first to the scalar 2D BPM. It is also extended to calculate the sensitivities of 3D structures using full vectorial BPM. The proposed approach achieves a significant time saving in calculating the response and its sensitivities. The accuracy of our approach is verified through comparison with the expensive and accurate central finite difference applied directly at the response level. We also utilized the calculated sensitivities in gradient-based optimization algorithms to maximize the power coupling in 3D optical fiber coupler.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 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".