Capillary-Porous Materials

Physics-Informed Neural Networks (PINN) represent a powerful approach in machine learning that enables the solution of forward, inverse, and parameter identification problems related to models governed by fractional differential equations. This is achieved by incorporating residuals of operator equations, boundary, and initial conditions into the objective function during training.

It is proposed to refine the calculation of Nusselt numbers by considering the mass transfer coefficient in the evaporation zone, which is significantly larger than the molecular mass transfer coefficient of vapour.  This refinement aims to address the discrepancy between the elevated Nusselt criteria observed during drying and the criteria determined by the thickness of the boundary layer, which provides more accurate results.

A fractional neural network with an adaptive learning rate has been proposed for modeling the dynamics of non-isothermal heat and mass transfer in capillary-porous materials, taking into account the memory effect and spatial nonlocality. The proposed approach employs a decoupled neural network architecture based on loss functions that reflect the physical characteristics of the investigated process. A stepwise training method is utilized to reduce sensitivity to errors and disruptions.