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In order to model high-speed nonlinear circuits, recurrent neural network (RNN) has been widely used in computer-aided design (CAD) area to achieve high performance and fast models compared with the existing models. Despite their advantages, they still have challenges such as large training time and limited test accuracy. In this article, the batch normalization (BN) method is applied to deep RNN leading to a much shorter training time and more accurate models compared with the conventional RNN. The proposed BN-RNN method works by modifying the distribution of the internal nodes of a deep network in the training course as an internal auxiliary shift yielding a much faster training. Indeed, the internal covariance shift will be reduced and the training of deep neural networks will be accelerated via a normalization step applied to the layers of RNN. BN-RNN, moreover, has a beneficial effect on gradient flow through the grid by reducing the dependence of gradients on the scale of network parameters or their initial values. This provides a much better learning process without the risk of divergence. For verifying the proposed method, time-domain modeling of three high-speed nonlinear circuits operating at the GHz region is provided. Comparisons of the training and test errors between RNN and BN-RNN, and evaluation time comparisons between transistor level and the BN-RNN-based models for these circuits prove the higher speed of the models obtained from the BN-RNN method. In addition, it is shown that training using the proposed method requires much less CPU time and number of epochs. [ABSTRACT FROM AUTHOR]

This paper presents a novel sensitivity-analysis-based adjoint neural-network (SAANN) technique to develop parametric models of microwave passive components. This technique allows robust parametric model development by learning not only the input–output behavior of the modeling problem, but also derivatives obtained from electromagnetic (EM) sensitivity analysis. A novel derivation is introduced to allow complicated high-order derivatives to be computed by a simple artificial neural-network (ANN) forward-back propagation procedure. New formulations are deduced for exact second-order sensitivity analysis of general multilayer neural-network structures with any numbers of layers and hidden neurons. Compared to our previous work on adjoint neural networks, the proposed SAANN is easier to implement into an existing ANN structure. The proposed technique allows us to obtain accurate and parametric models with less training data. Another benefit of this technique is that the trained model can accurately predict derivatives to geometrical or material parameters, regardless of whether or not these parameters are accommodated as sensitivity variables in EM simulators. Once trained, the SAANN models provide accurate and fast prediction of EM responses and derivatives used for high-level optimization with geometrical or material parameters as design variables. Three examples including parametric modeling of coupled-line filters, cavity filters, and junctions are presented to demonstrate the validity of this technique. [ABSTRACT FROM AUTHOR]