The paper presents a method to solve singular non-linear system representing polytrophic and isothermal sphere using neural network optimized by evolutionary computational approach. A trial solution of the system is written as a feed-forward neural network containing adaptive parameters (weights and biases). We prepare a fitness evaluation function defining unsupervised error. The optimization of the error defines the accuracy in the model that is highly stochastic in nature. Genetic algorithm is exploited as a tool for global convergence and active set algorithm as a rapid local search. The given scheme is tested on the model with polytrophic index 5=λ . A comparative study is made with exact and optimal Homtopy asymptotic method. The stability and reliability of the proposed scheme is investigated by a comprehensive statistical analysis. The proposed results are found to be in good agreement with exact solution as well as numerical solvers.