Advanced competent Bayesian regularization neural network for mathematical modeling of the immune diabetes regulation system

In this research, the numerical investigations of the fractional order immune diabetes regulation system by using a competent Bayesian regularization neural network procedure have been provided. The fractional order derivatives are used to get better results in comparison with the integer order. The division of the mathematical system is performed in resting and activated macrophages, and the antigen, autolytic, and beta cells. The data generalization is accessible by using the traditional Adam scheme in order to decrease the mean square error, while the data is separated into testing 16%, training 70%, and substantiation 14%. The designed neural network structure is updated by using the optimization tests through Bayesian regularization, a single layer sigmoid activation function, and twenty-five neurons. As conventional modeling schemes depend on shortening traditions or linear calculations, while the stochastic BRNN can perform complicated data patterns and deliver precise calculations of system performance. The correctness of the designed optimizer is obtained through the overlapping of the outcomes and lesser absolute error for each class of the model. Moreover, few curves based on state transitions, regression, error histograms provide the competences of the proposed solver.