Accurate Analytic Equation Generation for Compact Modeling with Physics-Assisted Kolmogorov-Arnold Networks
Bibliographic record
Abstract
This article proposes a method to generate accurate and concise analytic equations for device compact modeling using Physics-Assisted Kolmogorov–Arnold Networks (PKAN). The equations are directly extracted from the trained neural network architecture. PKAN uses variable activation functions informed by prior physical knowledge to model device behaviors. Similarity constraints map these trained activation functions to mathematical symbols. Sparsification techniques simplify the network structure, producing concise and explicit equations. This article also presents four approaches for physics-assisted device modeling using PKAN: (1) generating entire continuous equations without human intervention, (2) applying correlation factors to existing models without requiring knowledge of internal physical mechanisms, (3) revising specific parts of existing models, and (4) automatically extending existing models. Experimental results show that PKAN demonstrates significant accuracy improvements, achieving error reductions of 91.8%, 91.5%, 66.2%, and 83.7% for corresponding experiments, respectively. These findings demonstrate PKAN’s potential for various device modeling applications. By combining the precision of neural networks with the clarity of symbolic representation, PKAN offers a powerful tool for device modeling 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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 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".