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This article presents a methodology to solve a one-dimensional steady-state nonlinear reactive transport model (RTM) that is meant for fluid and solute transport model of soft tissues and microvessels. The methodology integrates the artificial neural network (ANN), genetic algorithms (GAs), and pattern search (PS) aided by active-set technique (AST) and interior-point technique (IPT). The RTM is represented with nonlinear second-order system based on the boundary value problem of ordinary differential equation. The ANN modeling is used for governing expression of RTM to form a fitness function in mean square sense, and optimization solvers based on the GA, PS, GA-AST, GA-IPT, PS-AST, PS-IPT are used for viable learning of weights. Proposed techniques are applied to different nonlinear RTMs based on variation in the characteristic reaction rate and half-saturation concentration. The proposed stochastic numerical solutions are compared with state-of-the-art solvers in order to check the accuracy and convergence based on sufficient large multiple runs of the algorithms. [ABSTRACT FROM AUTHOR]

The present study investigate the numerical solution of nonlinear singular system represented with sixth Painlev́e equation by the strength of artificial intelligence using feed-forward artificial neural networks (ANNs) optimized with genetic algorithms (GAs), interior point technique (IPT), sequential quadratic programming (SQP), and their hybrids. The ANN provided a compatible method for finding nature-inspired mathematical model based on unsupervised error for sixth Painlev́e equation and adaptation of weights of these networks is carried out globally by the competency of GA aided with IPT or SQP algorithms. Moreover, a hybrid approach has been adopted for better proposed numerical results. An extensive statistical analysis has been performed through several independent runs of algorithms to validate the accuracy, convergence, and exactness of the proposed scheme. [ABSTRACT FROM AUTHOR]