A Meyer wavelet neural networks procedure for prediction, pantograph and delayed singular models

• A stochastic novel solver ANNs-GA-ASA is presented successfully for the numerical experimentations of the nonlinear biological LD nonlinear system. • The log-sigmoid function is used as an activation/merit function for solving the mathematical LD system. • The optimization of an error-based fitness function is presented using the hybrid computing framework GA-ASA. • The correctness of the proposed ANNs-GA-ASA procedures are observed by comparing the obtained results and the reference solutions. • The precision of the ANNs-GA-ASA is judged by finding the small AE for solving the mathematical LD system. • For the stability of the proposed numerical ANNs-GA-ASA scheme, the statistical analysis in terms of variance account for (VAF), Theil’s inequality coefficient (TIC) semi-interquartile (SIR) and mean absolute deviation (MAD) is provided. This work aims the numerical solutions of the nonlinear form of prediction, pantograph, and delayed differential singular models (NPPD-DSMs) by exploiting the Meyer wavelet neural networks (MWNNs). The optimization is accomplished using the local and global search paradigms of active-set approach (ASA) and genetic algorithm (GA), i.e., MWNNs-GA-ASA. An objective function is designed using the NPPD-MSMs and the corresponding boundary conditions, which is optimized through the GA-ASA paradigms. The obtained numerical outcomes of the NPPD-MSMs are compared with the true results to observe the correctness of the designed MWNNs-GA-ASA. The absolute error in good measures, i.e., negligible, for solving the NPPD-DSMs is plotted, which shows the stability and effectiveness of the MWNNs-GA-ASA. For the reliability of the procedure, the performances through different statistical operators have been presented for multiple trials to solve the NPPD-NSMs. Mathematics Subject Classification. Primary 68T07; Secondary 03D15, 90C60.