In this paper, novel computing approach using three different models of feed-forward artificial neural networks (ANNs) are presented for the solution of initial value problem (IVP) based on first Painlevé equation. These mathematical models of ANNs are developed in an unsupervised manner with capability to satisfy the initial conditions exactly using log-sigmoid, radial basis and tan-sigmoid transfer functions in hidden layers to approximate the solution of the problem. The training of design parameters in each model is performed with sequential quadratic programming technique. The accuracy, convergence and effectiveness of the proposed schemes are evaluated on the basis of the results of statistical analyses through sufficient large number of independent runs with different number of neurons in each model as well. The comparisons of these results of proposed schemes with standard numerical and analytical solutions validate the correctness of the design models. exact solution of first Painlevé equation reference results with fully explicit Runge–Kutta method approximate neural networks solution approximate solution u ˆ ( x ) using log-sigmoid activation function approximate solution u ˆ ( x ) using radial basis activation function approximate solution u ˆ ( x ) using tan-sigmoid activation function approximate neural networks solution with exactly satisfying initial conditions approximate solution u ˜ ( x ) using log-sigmoid activation function approximate solution u ˜ ( x ) using radial basis activation function approximate solution u ˜ ( x ) using tan-sigmoid activation function approximate analytical solution approximate solution y(x) with Homotopy perturbation method approximate solution y(x) with variational iterational method approximate solution y(x) with modified Homotopy perturbation method the root mean square error associated with differential equation objective or fitness function global root mean square error associated with the differential equation global mean square error mean fitness unknown weight vector 
Exactly satisfying initial conditions neural network models for numerical treatment of first Painlevé equation