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

Author

Listed:
  • Adiqa Kausar Kiani

    (Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan)

  • Wasim Ullah Khan

    (A School of Electrical Engineering and Automation, Wuhan University, East Lake South Road No. 8, Wuhan 430072, China)

  • Muhammad Asif Zahoor Raja

    (Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan
    Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan)

  • Yigang He

    (A School of Electrical Engineering and Automation, Wuhan University, East Lake South Road No. 8, Wuhan 430072, China)

  • Zulqurnain Sabir

    (Department of Mathematics and Statistics, Hazara University, Mansehra 21120, Pakistan)

  • Muhammad Shoaib

    (Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan)

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.

Suggested Citation

  • Adiqa Kausar Kiani & Wasim Ullah Khan & Muhammad Asif Zahoor Raja & Yigang He & Zulqurnain Sabir & Muhammad Shoaib, 2021. "Intelligent Backpropagation Networks with Bayesian Regularization for Mathematical Models of Environmental Economic Systems," Sustainability, MDPI, vol. 13(17), pages 1-19, August.
    • Handle: RePEc:gam:jsusta:v:13:y:2021:i:17:p:9537-:d:621166
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    2. Zulqurnain Sabir & Atef F. Hashem & Adnène Arbi & Mohamed A. Abdelkawy, 2023. "Designing a Bayesian Regularization Approach to Solve the Fractional Layla and Majnun System," Mathematics, MDPI, vol. 11(17), pages 1-13, September.
    3. Songyue Yu & Baoqiang Yan, 2022. "Existence and Multiplicity of Solutions for a Class of Particular Boundary Value Poisson Equations," Mathematics, MDPI, vol. 10(12), pages 1-19, June.

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