#### Article
###### Abstract  
In the paper, the author deals with modeling the stochastic behavior of ordinary patch antennas in terms of the mean and standard deviation of their reflection coefficient \(\mid\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! the measurements of two series of patch antenna arrays to extract the probability density function of design random variables. The measurements were performed in the C, X, and Ka bands. The author extracts the uncertainty of geometrical design parameters. It has a chief impact on the mean and standard deviation of the reflection coefficient of the manufactured antennas. This impact increases with growing frequency since geometrical uncertainty becomes a bigger fraction of the wavelength. The author derives an Artificial Neural Network (ANN) to model the mean and standard deviation of the reflection coefficient of ordinary patch antennas for the 24.5-28.7 GHz frequency band, which covers almost the entire n257 and n258 bands of the 5G spectrum. The data for training and testing the ANN are obtained by performing Finite-Difference Time-Domain simulations and a Polynomial Chaos Expansion (PCE) analysis of the antenna reflection coefficient for a predefined set of nominal values of random design parameters of the antenna. The PCE is an alternative to the Monte Carlo analysis and has been described and reviewed in detail in the present literature, e.g., [9; 10; 11]. The author implements a non-intrusive PCE analysis, as in [12], which deals with making multiple FDTD simulation runs for a set of realizations of design random variables. The author uses a free openEMS Matlab-based package [13] for the FDTD computations. The FDTD simulation results are applied to the spectral projection process to derive PCE meta-models whose coefficients are applied directly to calculate the mean and standard deviation of \(\,\mid\!S_{11}\!\mid\,\). The author performs PCE computations using a free Matlab-based package called UQLab [14]. Each FDTD simulation is a very time-consuming process, e.g., computing the mean and standard deviation of \(\,\mid\!S_{11}\!\mid\,\) may require 10 or more FDTD simulation runs for each set of nominal values of design random variables, depending on the size of the support of these random variables. The author uses a method for a substantial reduction of the number of FDTD simulation runs required to compute PCE meta-models associated with the predefined nominal values of geometrical antenna design parameters. It is based on the author's analytical transformations and proper segmentation of the support of those design random variables. The aforementioned method was introduced in [15] where it was used with the uniform theory of diffraction (UTD) for worst-case analysis in a wireless telecommunication channel. In this paper, the method is applied and adjusted for the first time to FDTD-PCE computations. The novel application of the method enables a large reduction of the absolute FDTD-PCE computations time. This time reduction can be counted in days. Each PCE meta-model is formed by its coefficients, as well as by corresponding polynomials, which are orthogonal with respect to the probability density function of random design variables [9]; however, only the coefficients are required to compute the mean and standard deviation associated with the PCE meta-model. The author reduces the required number of these coefficients for each PCE meta-model by performing the sensitivity analysis using the Sobol Indices up to the second-order, as in [16]. The application of ANNs for coding the results of FDTD simulations in the area of electromagnetic (EM) fields was the subject of the literature in the past, e.g., in [17; 18; 19], where ANN is used to derive surrogate models that conform to the FDTD simulation results. In [17; 18], two-stage ANN coding is presented for a case of high dimensionality input data, while in [19], the authors use the ANN to model the scattering parameters of microstrip radio-frequency devices by taking into account deterministic design variables.