Systematic Neuro-Transfer Function Parametric Modeling With a Compact Embedded Format

This research proposes a systematic neuro-transfer function (neuro-TF) parametric modeling with a compact embedded format. Introducing transfer functions significantly enhances the capability of neural networks for electromagnetic (EM) parametric modeling. For modeling data based on vector fitting processing, the subtransfer function (sub-TF) response represented by each pole-residue pair exhibits different physical properties and data characteristics. Embedding the transfer function in the neural network enables good modeling accuracy for the strongly resonant sub-TF response, but for the nonstrongly resonant sub-TF response the poles/residues change abruptly as the geometrical parameters vary. This discontinuity issue of transfer function parameters for nonstrong resonance results in poor robustness and modeling accuracy. We propose a compact form of partially embedding the transfer function in neural networks to systematically solve this problem without introducing any other functions and structures. To accurately judge the embedding range, we propose an embedding range judgment algorithm based on resonance degree. We outline the training process and derive the corresponding derivative formula to expedite gradient-based training convergence. The proposed method uses a compact embedded format to achieve good modeling accuracy compared to existing neuro-TF methods, even including methods that introduce other functions and structures. Three modeling examples of microwave components verify the effectiveness and robustness of the proposed method.