Efficient FEM-Based EM Optimization Technique Using Combined Lagrangian Method With Newton’s Method
Bibliographic record
Abstract
Gradient-based optimization algorithms are popularly used in electromagnetic (EM)-based design optimizations. Among the gradient-based optimization algorithms, Newton's method is not practically applicable to EM optimization because it is very time consuming to obtain the Hessian matrix containing the second-order derivatives of the EM responses with respect to the geometrical variables. This article addresses this situation and proposes an efficient gradient-based EM optimization technique using the combined Lagrangian method with Newton's method. EM optimizations can be reformulated into constrained optimizations when the finite element method (FEM) is applied to perform EM simulations. In this article, we propose to elevate the Lagrangian method (i.e., a popular constrained optimization method) to EM optimization. By using the Lagrangian method to perform the EM optimization, the Hessian matrix can be obtained efficiently without the time-consuming evaluations of second-order derivatives of the EM responses with respect to the geometrical variables. With the efficiently calculated the Hessian matrix, Newton's method can be applied. We derive new formulations of Newton's method specifically for the EM optimization with the Lagrangian method. The proposed EM optimization using the combined Lagrangian method with Newton's method can converge faster than direct EM optimizations with other gradient-based optimization methods. The proposed technique is demonstrated by two EM optimization examples of microwave components.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".