Estimating Space-Dependent Coefficients for 1D Transport using Gaussian Processes as State Estimator in the Frequency Domain

This letter presents a method to estimate the space-dependent transport coefficients (diffusion, convection, reaction, and source/sink) for a generic scalar transport model, e.g. heat or mass. As the problem is solved in the frequency domain, the complex valued state as a function of the spatial variable is estimated using Gaussian process regression. The resulting probability density function of the state, together with a semi-discretization of the model, and a linear parameterization of the coefficients are used to determine the maximum likelihood solution for these space-dependent coefficients. The proposed method is illustrated by simulations.