Surrogate Modeling With Complex-Valued Neural Nets for Signal Integrity Applications

Neural networks (NNs) are quite attractive in creating surrogate models for many signal integrity (SI) applications. NN-based surrogate models offer the benefits of reducing the design cycle time and providing the designer with a quick prototype that can efficiently analyze the performance of the SI task. This article, therefore, proposes a new end-to-end learning approach for surrogate modeling using complex-valued NNs, incorporating higher functionality and better representation. This approach introduces a deep complex dense network (<inline-formula> <tex-math notation="LaTeX">$\mathbb{C}$</tex-math> </inline-formula>DNet), which is built with complex dense blocks to support complex operations using complex-valued weights, and a physically consistent layer to enforce passivity and causality constraints. We also present a robust inverse multiobjective optimization method to minimize the modeling error and optimize the design space parameters. The results show that our model outperforms state-of-the-art deep surrogate models when tasked with forward and inverse learning for a relatively small amount of data. The effectiveness of the proposed approach is demonstrated through two SI design applications, where the model is used to predict broadband <inline-formula> <tex-math notation="LaTeX">$S$</tex-math> </inline-formula>-parameters and obtain optimal design space parameters given the desired target specifications.