A dual-layered neural network for the cancer system with stem cells and chemotherapy

Purpose The present research investigations provide the numerical performances of the cancer system with stem cell and chemotherapy by using a dual-layered stochastic process. The mathematical cancer system with chemotherapy along with stem cells is one of the nonlinear models, which are classified into four different cell groups, called as stem S(x), effected E(x): tumor T(x), and chemotherapy having concentration drug M(x). Method A design of deep neural network having two different layers is presented by using sigmoid function in both hidden layers, with 15 and 20 numbers of neurons in the respective layers, while the optimization is performed through the Bayesian regularization scheme, which is considered an effective approach for solving the nonlinear models. The construction of the dataset is performed through the implicit Runge–Kutta approach, which reduces the mean square error by separating into training as 70%, testing 16%, and verification 14%. Results The dual-layered neural network solver’s correctness is performed by using the comparison of the results, and best training is around 10^–09 to 10^–11, and negligible absolute error is found as 10^–06 to 10^–08. Moreover, some tests including regression, transition state, best fitness, and error histogram also update the consistency of the designed dual-layered procedure. Novelty A design of deep neural network having two different layers is first time applied to solve the cancer system with stem cell and chemotherapy.