Neural Networks for the Estimation of Low-Order Statistical Moments of a Stochastic Dielectric

Paper in proceeding, 2021

We present two different machine learning strategies to estimate the two lowest-order statistical moments of a two-dimensional inhomogeneous dielectric medium with stochastic variations, which have a Gaussian distribution for every point in the measurement region and a Gaussian auto-covariance function. In particular, we consider and compare (i) a fully-connected neural network and (ii) an affine model. These are trained to predict the pointwise mean and standard deviation of the underlying stochastic dielectric based on the scattering parameters, which are computed at the ports of four sensors that are placed around the circumference of the two-dimensional measurement region. We use the mean and variance of the real and imaginary part of the scattering parameters in a feature-extraction step before training. It is demonstrated that both machine learning strategies predict the mean permittivity well. However, the neural network outperforms the affine model for the prediction of the standard deviation. In addition, this article reviews the workflow for training, validating and testing a neural network in the context of measurement applications, where the ambition is to give an introduction to practitioners who would like to explore neural networks for their measurement application.