Detail flow diagram of processes for obtaining the proposed solution of FP equation using neural networks trained with hybrid approach GA-SQP.

Novel stochastic solver for boundary value problems of Flierl–Petvishivile equations.

Strength of model is to avoid singularity and satisfy the conditions for unbounded domain.

The accuracy of the approach is validated on three variants of two nonlinear problems.

Detail simulations are performed to evaluate the reliability and effectiveness.