Modeling Electrically Long Interconnects Using Physics-Informed Delayed Gaussian Processes
Bibliographic record
Abstract
This work presents a machine learning technique to model wide-band scattering parameters (S-parameters) of interconnects in the frequency domain using a new Gaussian processes (GP) model. Standard GPs with a general-purpose kernel typically assume high smoothness and therefore are not suitable to model S-parameters that are highly dynamic and oscillating due to propagation delays. The new delayed Gaussian process ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\tau$</tex-math></inline-formula> GP) model employs a physics-informed kernel consisting of periodic components, whose fundamental frequencies are interpreted as tunable propagation delays. Then, the model hyperparameters are tuned using a combination of maximum marginal likelihood estimation (MMLE) and delay estimation using Gabor transform. The delay estimation allows one to automatically identify the optimal fundamental frequencies for the kernel, thus increasing the numerical stability of the hyperparameters tuning process. The resulting delayed Gaussian process model accurately predicts the S-parameter values at desired frequency points in the training interval. Two application examples demonstrate the increased accuracy of the new technique, compared to standard Gaussian processes, vector fitting (VF), and delayed vector fitting (DVF) rational models.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".