fractional derivatives

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.

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.