Physics-Informed Neural Network for Modeling the Process of Heat-and-Mass Transfer Based on the Apparatus of Fractional Derivatives

One- and two-dimensional mathematical models of anisotropic non-isothermal moisture transfer, based on the use of the Caputo and Grünwald-Letnikov fractional operators, were considered and improved. In order to find a numerical solution of interrelated differential equations, a neural network structure with a disconnected network architecture is proposed to determine the evolution of moisture and temperature fields based on a loss function containing physical information about the process under study. Fractional differential calculation formulas are used to represent fractional operators, as well as difference schemes for loss functions are constructedA method for network learning is proposed that smooths out the instability inherent in optimization processes in deep neural networks. Software for the implementation of a fractal neural network was developed and the obtained numerical results were compared with the results obtained using finite difference numerical methods. The effectiveness of the developed method is substantiated.