Macromodeling of Nonlinear High-Speed Circuits Using Novel Hybrid Bidirectional High-Order Deep Recurrent Neural Network

A new structure and macromodeling approach which is an advance over high-order recurrent neural network named bidirectional high-order deep recurrent neural network (BIHODRNN) is proposed in this paper for the first time for nonlinear circuits. In the proposed structure, besides the fully connected weights to the neurons of multiple previous time steps of the same hidden layer in conventional high-order recurrent neural network (HORNN), there are additional fully connected weights to the neurons of that hidden layer for multiple next times steps. Due to more training parameters compared to conventional RNN and HORNN, the proposed BIHODRNN can train and predict more complex relationships in a faster and more efficient way and can better capture long-term dependencies. Also, because of bidirectional structure with multiple orders to the next time steps, it can predict the output signals beyond the training time intervals with much better accuracy. To improve the accuracy of the proposed BIHODRNN even more, another structure and method called Hybrid BIHODRNN was presented in this paper. By combining layers of different orders and different directionality in Hybrid BIHODRNN, the training parameters are significantly decreased leading to the reduction of overfitting problem and increasing the model accuracy. Furthermore, the proposed BIHODRNN and its hybrid version need smaller number of training data compared to the HODRNN for generating a model with similar accuracy. Moreover, two proposed approaches are notably faster than the transistor-level models in circuit simulators for acquiring similar accuracy. The superiorities of the proposed approaches are investigated by modeling two nonlinear circuit examples, namely, 5-coupled and 3-coupled line high-speed interconnects both driven by a four-stage driver.