Power-Ground Plane Impedance Modeling Using Deep Neural Networks and an Adaptive Sampling Process

—This paper proposes a deep neural network (DNN) based method for the purpose of power-ground plane impedance modeling. A composite DNN model, which is a combination of two DNNs is used to predict the Z-parameters of power ground planes from their design parameters. The first DNN predicts the normalized Z-parameters whereas the second DNN predicts the original maximum and minimum values of the non-normalized Z-parameters. This allows the method to retain a high accuracy when predicting responses that have large variations across designs, as is the case with the Z-parameters of the power-ground planes. We use the adaptive sampling algorithm to generate the training and validation samples for the DNNs. The adaptive sampling algorithm starts with only a few samples, then slowly generates more samples in the non-linear regions within the design parameters space. The level of non-linearity of the regions is determined by a surrogate model which is also trained using the generated samples as well. If the surrogate model has poor prediction accuracy in a region, then the adaptive sampling algorithm will generate more samples in that region. A shallow neural network is used as the surrogate model for non-linearity determination of the regions since it is faster to train and update. Once all the samples have been generated, they will be used to train and validate the composite DNN models. Finally, we present two examples, a square-shaped power ground plane and a square-shaped power ground plane with a hollow square at the center to demonstrate the robustness of the DNN composite models.