Efficient transient simulation of networks containing lossy frequency-dependent interconnects
Bibliographic record
Abstract
Since the introduction of the Asymptotic Waveform Evaluation algorithm [1], model order reduction techniques have shown high computational efficiency for fast solution of large interconnect problems. The reduced-order models of linear interconnect networks can be derived by matching network moments via Pade approximations. For interconnect networks containing distributed transmission lines, the associated moments can be generated by using the eigenvalue moment method [2] or the matrix exponential method [3]. In the former method, the moments are generated by computing eigenvalues and eigenvectors of the transmission line propagation matrix. It is noticed, however, that the accuracy of the moments calculated by using the eigenvalue moment method decreases with the increase of moment order due to the truncation error in evaluation of the eigenvalues and eigenvectors. Accurate generation of moments is critical in applying moment matching techniques to interconnect analysis since small errors in the moments can considerably affect the accuracy of the simulation results. In order to obtain more accurate transmission line moments, one can apply the matrix exponential method. In this method, the moments are obtained by expanding the transmission line parameter matrix as a Taylor series. The moments of transmission lines with frequency-dependent parameters can be computed in the same manner [4]. Although the matrix exponential method can generate more accurate moments, it is computationally more costly than the eigenvalue moment method due to the slow convergence of the matrix exponential series.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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) | 0.003 | 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".