One crucial and intricate problem in the education sector that must be dealt with is children who initially enrolled in schools but later dropped out before finishing mandatory primary education. These children are generally referred to as out-of-school children. To contribute to the discuss, this paper presents the development of a robust Multilayer Perceptron (MLP) based Neural Network Model (NN) for optimal prognostic learning of out-of-school children trends in Africa. First, the Bayesian optimization algorithm has been engaged to determine the best MLP hyperparameters and their specific training values. Secondly, MLP-tuned hyperparameters were employed for optimal prognostic learning of different out-of-school children data trends in Africa. Thirdly, to assess the proposed MLP-NN model's prognostic performance, two error metrics were utilized, which are the Correlation coefficient (R) and Normalized root means square error (NRMSE). Among other things, a higher R and lower NRMSE values indicate a better MLP-NN precision performance. The all-inclusive results of the developed MLP-NN model indicate a satisfactory prediction capacity, attaining low NRMSE values between 0.017 - 0.310 during training and 0.034 - 0.233 during testing, respectively. In terms of correlation fits, the out-of-school children's data and the ones obtained with the developed MLP-NN model recorded high correlation precision training/testing performance values of 0.9968/0.9974, 0.9801/0.9373, 0.9977/0.9948 and 0.9957/0.9970, respectively. Thus, the MLP-NN model has made it possible to reliably predict the different patterns and trends rate of out-of-school children in Africa. One of the implications for counselling, among others, is that if every African government is seriously committed to funding education at the foundation level, there would be a reduction in the number of out-of-school children as observed in the out-of-school children data.