Nonlinear Circuit Macromodeling Using New Heterogeneous-Layered Deep Clockwork Recurrent Neural Network

Nonlinear circuit modeling is a complex task involving sequential data and time-domain analysis. While Recurrent Neural Networks (RNNs) handle these tasks, their limitations include low test accuracy and extended training times. Deep time-domain networks, like deep recurrent neural networks (DRNNs) and deep long short-term memory (DLSTM), aim to address these limitations but bring challenges such as long training times, the vanishing gradient problem, overfitting, and significant test errors due to their large number of parameters. This paper proposes a novel structure and macromodeling approach for nonlinear circuits based on deep clockwork recurrent neural networks (DCWRNNs). Deep CWRNNs offer better feature extraction capability than their shallow counterparts and can generate more accurate and faster models than conventional DRNN and DLSTM. Its unique structure with deep modules operating at different clock periods facilitates better extraction of high and low-frequency information, resulting in smaller test errors. A Heterogeneous-layered DCWRNN (HL-DCWRNN) is also introduced, adjusting module rates of each layer separately to enhance accuracy and mitigate overfitting. DCWRNN-based models require less computation effort (20-30 speedup reported) than transistor-level circuit simulator models. Validation through modeling two nonlinear high-speed interconnect circuits confirms the method's efficacy compared to DRNN, DLSTM, and shallow CWRNN methods.