A Physics-Informed Surrogate Model for the Bi-Flux Bevilacqua–Galeão Anomalous Diffusion Equation

Accurate modeling of bi-flux anomalous diffusion presents significant computational challenges in engineering. This paper investigates the effectiveness of physics-informed neural networks as surrogate models for the bi-flux anomalous diffusion equation. We investigate one-dimensional linear and nonlinear cases. Optimal hyperparameter configurations are determined using a modified differential evolution algorithm, guided by an objective function that leverages a combination of loss values. This optimization approach enables a rigorous evaluation of different neural network setups, providing valuable insights and practical guidance for researchers working with bi-flux anomalous diffusion phenomena. A comparison between physics-informed neural networks and conventional multilayer perceptrons is presented for the analyzed model. Finally, the capability of the best-performing models to act as virtual sensors is evaluated. This work provides guidance on the use of neural networks to efficiently and accurately tackle complex bi-flux anomalous diffusion problems, potentially accelerating research and development in fields where such processes are critical.