A method is proposed for determining the parameters of the vertically inhomogeneous diffusion coefficient in the atmospheric boundary layer based on matching data from numerical modeling of the dynamics of fine dust fractions and measurement results from quasi-periodic dust sources. The fitting of modeled and measured dust concentration time series is carried out using neural network modeling. An analysis of the influence of the neural network architecture choice and training procedure on the efficiency of atmospheric state reconstruction is presented. Data fitting is performed for several time series of dust concentrations of different particle diameters. We include the dispersion composition of dust into consideration when modeling its dynamics, which allows us to improve the reconstruction of the vertical profile of turbulent diffusion.