Exactly satisfying initial conditions neural network models for numerical treatment of first Painlev equation
A new stochastic intelligence method is developed to solve first Painlev equation. Design of three unsupervised ANN models that satisfying exactly initial conditions. Optimization capability of SQP is exploited for training of design parameter of ANNs. Accuracy and convergence are validated in term of various performance criterions. Impact on effectiveness of the models is investigated by varying neurons in ANNs.
neural network painlev transcendents sequential quadratic programming nonlinear differential equations activation functions