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Sustainability
Volume 13
Issue 17
10.3390/su13179537
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Article

Intelligent Backpropagation Networks with Bayesian Regularization for Mathematical Models of Environmental Economic Systems

by
Adiqa Kausar Kiani
1,
Wasim Ullah Khan
2,
Muhammad Asif Zahoor Raja
1,3,
Yigang He
2,*,
Zulqurnain Sabir
4 and
Muhammad Shoaib
5
1
Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan
2
A School of Electrical Engineering and Automation, Wuhan University, East Lake South Road No. 8, Wuhan 430072, China
3
Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan
4
Department of Mathematics and Statistics, Hazara University, Mansehra 21120, Pakistan
5
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan
*
Author to whom correspondence should be addressed.
Academic Editor: Magdalena Tutak
Sustainability 2021, 13(17), 9537; https://doi.org/10.3390/su13179537
Received: 14 May 2021 / Revised: 17 June 2021 / Accepted: 18 June 2021 / Published: 25 August 2021
(This article belongs to the Special Issue The Application of Numerical Methods and IT Tools to Environment and Safety Engineering)
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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. View Full-Text
Keywords: environmental economic system; backpropagation networks; Bayesian regularization; Adams numerical solver; regression index environmental economic system; backpropagation networks; Bayesian regularization; Adams numerical solver; regression index
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MDPI and ACS Style

Kiani, A.K.; Khan, W.U.; Raja, M.A.Z.; He, Y.; Sabir, Z.; Shoaib, M. Intelligent Backpropagation Networks with Bayesian Regularization for Mathematical Models of Environmental Economic Systems. Sustainability 2021, 13, 9537. https://doi.org/10.3390/su13179537

AMA Style

Kiani AK, Khan WU, Raja MAZ, He Y, Sabir Z, Shoaib M. Intelligent Backpropagation Networks with Bayesian Regularization for Mathematical Models of Environmental Economic Systems. Sustainability. 2021; 13(17):9537. https://doi.org/10.3390/su13179537

Chicago/Turabian Style

Kiani, Adiqa K., Wasim U. Khan, Muhammad A.Z. Raja, Yigang He, Zulqurnain Sabir, and Muhammad Shoaib. 2021. "Intelligent Backpropagation Networks with Bayesian Regularization for Mathematical Models of Environmental Economic Systems" Sustainability 13, no. 17: 9537. https://doi.org/10.3390/su13179537

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