Neural Network for Modeling the Process of Moisture Transfer in Materials with Fractal Structure

Based on the apparatus of fractional integro-differentiation, a mathematical model of moisture transport in media with a fractal structure is considered for both one-dimensional and two-dimensional cases. A new convolutional learning architecture, based on existing data, is proposed for numerical modeling and behavior assessment of the dynamic process. This architecture is grounded in the fractal Euler method and the finite difference method. Initial and boundary conditions are tightly integrated into the network architecture, and residual connections, which explicitly model time progression and account for the fractional order of the time derivative, further enhance the model. Numerical results obtained using the developed software confirm the effectiveness of the proposed method in terms of solution accuracy.