Mathematical models of heat and moisture transfer for anisotropic materials, based on the use of the fractional calculus of integro-differentiation, are considered because such two-factor fractal models have not been proposed in the literature so far. The numerical implementation of mathematical models for determining changes in heat exchange and moisture exchange is based on the adaptation of the fractal neural network method, grounded in the physics of processes. A fractal physics-informed neural network architecture with a decoupled structure is proposed, based on loss functions informed by the physical process under study. Fractional differential formulas are applied to the expressions of non-integer operators, and finite difference schemes are developed for all components of the loss functions. A step-by-step method for network training is proposed. An algorithm for the implementation of the fractal physics-informed neural network is developed. The efficiency of the new method is substantiated by comparing the obtained numerical results with numerical approximation by finite differences and experimental data for particular cases.

In this paper, we consider the possibilities of applying the theory of cellular automata when determining the changes of the temperature and humidity of air masses in the CAD model of a wood drying chamber. Also, in this paper describes the developed software, which allows us to present the CAD model of a wood drying chamber in the form of a three-dimensional array. The elements of this array are 3D cubes, each of which has six faces. All these faces can interact with other faces, both own and adjacent object of class 3D cube. The interconnections between these faces are given in the scheme of relations. In addition, the work describes the developed classes and gives diagrams of classes and sequences.

Mathematical model of heat and moisture transfer in the materials with fractal structure considering the effects of memory and spatial correlation are synthesized. Explicit and implicit difference schemes for related equations are built. A numerical method predictor-corrector for the implementation of the mathematical model of heat and moisture transfer in materials with fractal structure was introduced. The parallelization of algorithm of implementation this numerical method was proposed.

The two-dimensional mathematical model of rheological behavior of wood in non-isothermal moisture transfer conditions which consider the medium fractal structure, available memory and spatial correlation effects was synthesized. Difference schemes of differential equations of heat and moisture transfer and visco-elastic deformation in the two-dimensional area with appropriate boundary conditions was constructed. The algorithmic and software aspects for implementing the mathematical models using predictor-corrector method was obtained.

This work describes the calculation parameters of the drying agent, which includes the speed of air circulation, its temperature and humidity. The result of the calculation is the establishment of radial-basis artificial neural network, which allows to determine any parameter of drying agent at any point, represented by the coordinates X, Y, Z, and located within the drying chambers. Also in this work, it is given the calculation of extrapolation for existing parameters of drying agent, for their prediction. In addition, the graphics that display the changes of parameters of the drying agent were provided, according to the coordinates X, Y, Z and time moments.

Two-dimensional mathematical model of non-isothermal moisture transfer and viscoelastic deformation in the environments with fractal structure considering the effects of memory and spatial correlation are synthesized. Explicit and implicit difference schemes for related equations of heat and mass transfer in two-dimensional domain with boundary conditions of the third kind are built. The algorithmic aspects for implementation of obtained difference equations with the use of predictor-corrector method are presented and the conditions of stability of these difference schemes are analyzed.