Nonlinear dynamics system identification is crucial for circuit emulation. Traditional continuous-time domain modeling approaches have limitations in fitting capability and computational efficiency when used for modeling circuit IPs and device behaviors.This paper presents a novel continuous-time domain hybrid modeling paradigm. It integrates neural network differential models with recurrent neural networks (RNNs), creating NODE-RNN and NCDE-RNN models based on neural ordinary differential equations (NODE) and neural controlled differential equations (NCDE), respectively.Theoretical analysis shows that this hybrid model has mathematical advantages in event-driven dynamic mutation response and gradient propagation stability. Validation using real data from PIN diodes in high-power microwave environments shows NCDE-RNN improves fitting accuracy by 33\% over traditional NCDE, and NODE-RNN by 24\% over CTRNN, especially in capturing nonlinear memory effects.The model has been successfully deployed in Verilog-A and validated through circuit emulation, confirming its compatibility with existing platforms and practical value.This hybrid dynamics paradigm, by restructuring the neural differential equation solution path, offers new ideas for high-precision circuit time-domain modeling and is significant for complex nonlinear circuit system modeling.

翻译：非线性动力学系统辨识对于电路仿真至关重要。传统连续时域建模方法在用于电路IP与器件行为建模时，其拟合能力与计算效率存在局限。本文提出一种新颖的连续时域混合建模范式，将神经网络微分模型与循环神经网络（RNNs）相结合，分别构建了基于神经常微分方程（NODE）的NODE-RNN模型和基于神经控制微分方程（NCDE）的NCDE-RNN模型。理论分析表明，该混合模型在事件驱动的动态突变响应与梯度传播稳定性方面具有数学优势。利用高功率微波环境下PIN二极管的真实数据进行验证，结果显示NCDE-RNN相比传统NCDE模型拟合精度提升33\%，NODE-RNN相比CTRNN提升24\%，尤其在捕获非线性记忆效应方面表现突出。该模型已成功部署于Verilog-A并通过电路仿真验证，证实了其与现有平台的兼容性及实用价值。此混合动力学范式通过重构神经微分方程求解路径，为高精度电路时域建模提供了新思路，对复杂非线性电路系统建模具有重要意义。