Accurate Analytic Equation Generation for Compact Modeling with Physics-Assisted Kolmogorov-Arnold Networks

This paper 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 paper 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.