Dual Design: Inferring Structure from Fundamental Limits
Bibliographic record
Abstract
The recognition that the constraints implied by any set of linear differential equations can be reformulated to restate the optimization problems encountered in photonic inverse design as a quadratically constrained quadratic program (QCQP) and then convexified via Lagrange duality has proven to be a powerful means of determining fundamental performance limits. As soon as the constraints of total real and reactive power conservation are imposed, the subtle interplay between chosen material properties, device size, wave physics, and attainable objective values for basic scattering quantities is captured to a remarkable extent, including the onset of well-known asymptotics such as quasi-statics and geometric optics, and the possibility of creating resonances. More importantly, through the generalization of considering any number of local power conservation constraints, these convexification methods have been found to be remarkably predictive of what is possible for range of technologically relevant electromagnetic processes; limits coming within a factor of ten of topology optimized structures have been found for variety of basic absorption, scattering and field transformation functions as well as more complex objectives like surface-enhanced Raman scattering.
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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 | 0.004 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".