Uncertainty Quantification for PEEC Based on Wasserstein Generative Adversarial Network

This article proposes a modified generative adversarial network (GAN)-based approach, namely Wasserstein GAN (WGAN), for the uncertainty quantification (UQ) in partial equivalent element circuit (PEEC) models. Initially, the stochastic PEEC is constructed to obtain the sample data of the quantities of interest (QoI). This sample data, along with the fake data from the generator, serves as input for the discriminator in WGAN. The loss function of the generator in WGAN is constructed using the Wasserstein distance to provide a more usable gradient than that in the traditional GAN. By estimating the distribution of sample data using the fake data in the discriminator, the stochastic properties of the QoI can be finally obtained. Notably, the proposed method can efficiently estimate the stochastic characteristics of the QoI without prior knowledge of its probability distribution. Two numerical examples are provided to validate the proposed method. It is demonstrated that the proposed WGAN method effectively quantifies uncertainty in PEEC models. Compared to traditional methods, the proposed WGAN achieves a remarkable 20-fold increase in computational speed. Consequently, our work offers a powerful machine learning tool for advanced UQ in complex electromagnetic simulations.