Stochastic machine learning modeling for the estimation of some uncertain parameters. Case study: Retardation factor in a radionuclide transport model

In the present work, we define a stochastic model using machine learning techniques to generate random fields of some uncertain parameters. The proposed stochastic model is based on Bayesian inference and aims at reconstituting the parameters of interest and their credible intervals. The main goal of this work is to define a model that estimates the values of the uncertain parameters known only by their distribution probability functions and some observed spatial measurements. We note that this type of parameters may be associated with some mathematical models usually traduced by non-linear differential equations. In our case, we study the uncertainty of the retardation factor in a radionuclide transport model. To achieve a more realistic parameter estimation, Markov сhain Monte Carlo (MCMC) algorithms are applied. We demonstrate that the obtained results confirm the feasibility of our proposed model and lead to a new understanding of contaminants' behavior.