: 108-120
Received: August 12, 2023
Revised: September 28, 2023
Accepted: October 01, 2023
Lviv Polytechnic National University, Lviv, Ukraine
Ukrainian National Forestry University

In this paper, a mathematical model of moisture transfer in capillary-porous media in one- and two-dimensional space is presented and investigated, for its description the apparatus of fractional integrodifferentiation was used. This approach made it possible to take into account such properties of a system with a fractal structure as memory, self-organization, temporal and spatial correlations. The complexity of this mathematical model complicates its application and requires significant computing power. To calculate the numerical solution of the differential equation and speed up the calculations, the fractal neural network method, which is based on the fPINN architecture, is used. This method uses a loss function that takes into account physical information about the process under study. Formulas from fractional differential calculus were applied to express fractional derivatives and a difference scheme for the loss function was developed. The software for the implementation of the neural network method was developed and the applied approach was justified by comparing the obtained numerical results with the results of experiments by other scientists and the results obtained using finite difference numerical methods. The reliability check of the investigated indicators indicates the adequacy of the mathematical model and the prospects for further application of the numerical fractal neural network method.

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