A new approach to inpainting problems that combines domain decomposition methods (DDM) with deep neural networks (DNN) to solve partial differential equations (PDE) is presented. First, this article examines different
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-lin
The process of gas filtration in a porous medium depending on its structure is modeled in the paper. The presence of pores of various sizes leads to the formation of flow and stagnation zones, which affect both the pressure distribution in the medium and the active gas mass. The obtained results make it possible to determine the proportion of the flow zones volume and the exchange coefficient between the flow and stagnant zones.
The method of solving problems of mathematical physics, in particular for pressure distribution finding in the water in the underground gas storage layers on the basis of the biorthogonal polynomials constructed by the authors is proposed in the paper. The way of the problem solving by the method of separation of variables on the basis of the biorthogonal polynomials is studied. The solution of the problem is found in the form of the series sum of the biorthogonal and quasi-spectral polynomials. The comparative analysis for the different values of parameters is performed. The impact of