Abstract
The research community of environmental economics has had a growing interest for the exploration of artificial intelligence (AI)-based systems to provide enriched efficiencies and strengthened human knacks in daily live maneuvers, business stratagems, and society evolution. In this investigation, AI-based intelligent backpropagation networks of Bayesian regularization (IBNs-BR) were exploited for the numerical treatment of mathematical models representing environmental economic systems (EESs). The governing relations of EESs were presented in the form of differential models representing their fundamental compartments or indicators for economic and environmental parameters. The reference datasets of EESs were assembled using the Adams numerical solver for different EES scenarios and were used as targets of IBNs-BR to find the approximate solutions. Comparative studies based on convergence curves on the mean square error (MSE) and absolute deviation from the reference results were used to verify the correctness of IBNs-BR for solving EESs, i.e., MSE of around 10−9 to 10−10 and absolute error close to 10−5 to 10−7. The endorsement of results was further validated through performance evaluation by means of error histogram analysis, the regression index, and the mean squared deviation-based figure of merit for each EES scenario.
Highlights
Differential equations-based modeling is extensively use for measuring the behavior of complex systems representing different applications of applied sciences, engineering, and technologies
The comparative studies based on convergence curves on the mean square error, error histogram analysis, and regression index are used to verify further the correctness of the intelligent backpropagation networks of Bayesian regularization (IBNs-BR) for each environmental economic systems (EESs) scenario
Puting paradigm for the numerical treatment of mathematical models representing the environmental economic systems using the competency of intelligent backprop‐
Summary
Differential equations-based modeling is extensively use for measuring the behavior of complex systems representing different applications of applied sciences, engineering, and technologies. Victim”-type [11] mathematical models accurately represent their descriptions with the help of a liability differential system as follows [12]: dy dt dy dt dy dt. Where Ki is the ith function representation of inputs, y1 and y2 stand for economical strong countries or regions, while y3 is the low economic country representation with suitable conditions. Another environmental economic model based on three class nonlinear differential equations is given as [12]: Different mathematical representations are constructed for a variety of scenarios to predict the feasible situation more accurately [8,9,10].
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