A Unified Automated Parametric Modeling Algorithm Using Knowledge-Based Neural Network and ${l}_{1}$ Optimization

Abstract

Knowledge-based neural network modeling techniques using space-mapping concept have been demonstrated in the existing literature as efficient methods to overcome the accuracy limitations of empirical/equivalent circuit models when matching new electromagnetic data. For different modeling problems, the mapping structures can be different. In this paper, we propose a unified automated model generation algorithm that uses $\boldsymbol {l}_{\mathbf {1}}$ optimization to automatically determine the type and the topology of the mapping structure in a knowledge-based neural network model. By encompassing various types of mappings of the knowledge-based neural network model in the existing literature, we present a new unified model structure and derive new sensitivity formulas for the training of the unified model. The proposed $\boldsymbol {l}_{\mathbf {1}}$ formulation of modeling can force some weights of the mapping neural networks to zeros while leaving other weights as nonzeros. We utilize this feature to allow $\boldsymbol {l}_{\mathbf {1}}$ optimization to automatically determine which mapping is necessary and which mapping is unnecessary. Using the proposed $\boldsymbol {l}_{\mathbf {1}}$ optimization method, the mapping structure can be determined to address different needs of different modeling problems. The structure of the final knowledge-based model can be flexible combinations of some or all of linear mapping, nonlinear mapping, input mapping, frequency mapping, and output mapping. In this way, the proposed algorithm is more systematic and can further speed up the knowledge-based modeling process than existing knowledge-based modeling algorithms. The proposed method is illustrated by three microwave filter modeling examples.