A Novel Framework for Parametric Loewner Matrix Interpolation
Bibliographic record
Abstract
The generation of black-box macromodels of passive components at the chip, package, and board levels has become an important step of the electronic design automation (EDA) workflow. The vector fitting (VF) scheme is a very popular method for the extraction of such macromodels, and several multivariate extensions are now available for embedding external parameters in the model structure, thus enabling model-based variability analysis and design optimization. The Loewner matrix interpolation framework was recently suggested as an effective and promising alternative macromodeling approach to VF. In this article, we propose a parametric version of Loewner interpolation, which embeds orthogonal polynomials as an integral part of the parameterization framework. This approach is shown to be efficient and accurate and presents various advantages with respect to competing multivariate rational interpolation methods. These advantages include better control of model smoothness in the parameter space and a particularly efficient implementation of the singular value decomposition, which is the core of the model extraction scheme. These advantages are confirmed through several examples relevant for signal and power integrity applications.
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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 | 0.003 |
| 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 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
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".