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Step-by-step time discrete Physics-Informed Neural Networks with application to a sustainability PDE model

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  • Valentino, Carmine
  • Pagano, Giovanni
  • Conte, Dajana
  • Paternoster, Beatrice
  • Colace, Francesco
  • Casillo, Mario

Abstract

The use of Artificial Neural Networks (ANNs) has spread massively in several research fields. Among the various applications, ANNs have been exploited for the solution of Partial Differential Equations (PDEs). In this context, the so-called Physics-Informed Neural Networks (PINNs) are considered, i.e. neural networks generally constructed in such a way as to compute a continuous approximation in time and space of the exact solution of a PDE.

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  • Valentino, Carmine & Pagano, Giovanni & Conte, Dajana & Paternoster, Beatrice & Colace, Francesco & Casillo, Mario, 2025. "Step-by-step time discrete Physics-Informed Neural Networks with application to a sustainability PDE model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 230(C), pages 541-558.
    • Handle: RePEc:eee:matcom:v:230:y:2025:i:c:p:541-558
    DOI: 10.1016/j.matcom.2024.10.043
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    References listed on IDEAS

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    1. Barbosa-Póvoa, Ana Paula & da Silva, Cátia & Carvalho, Ana, 2018. "Opportunities and challenges in sustainable supply chain: An operations research perspective," European Journal of Operational Research, Elsevier, vol. 268(2), pages 399-431.
    2. Tang, Christopher S. & Davarzani, Hoda & Sarkis, Joseph, 2015. "Quantitative models for managing supply chain risks: A reviewAuthor-Name: Fahimnia, Behnam," European Journal of Operational Research, Elsevier, vol. 247(1), pages 1-15.
    3. Yue, Gentian & Wang, Lei & Zhang, Xin'an & Wu, Jihuai & Jiang, Qiwei & Zhang, Weifeng & Huang, Miaoliang & Lin, Jianming, 2014. "Fabrication of high performance multi-walled carbon nanotubes/polypyrrole counter electrode for dye-sensitized solar cells," Energy, Elsevier, vol. 67(C), pages 460-467.
    4. Amir Mosavi & Mohsen Salimi & Sina Faizollahzadeh Ardabili & Timon Rabczuk & Shahaboddin Shamshirband & Annamaria R. Varkonyi-Koczy, 2019. "State of the Art of Machine Learning Models in Energy Systems, a Systematic Review," Energies, MDPI, vol. 12(7), pages 1-42, April.
    5. Lior, Noam, 2008. "Energy resources and use: The present situation and possible paths to the future," Energy, Elsevier, vol. 33(6), pages 842-857.
    6. Dongsu Kim & Yeobeom Yoon & Jongman Lee & Pedro J. Mago & Kwangho Lee & Heejin Cho, 2022. "Design and Implementation of Smart Buildings: A Review of Current Research Trend," Energies, MDPI, vol. 15(12), pages 1-17, June.
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    1. Yuniel Martinez & Luis Rojas & Alvaro Peña & Matías Valenzuela & Jose Garcia, 2025. "Physics-Informed Neural Networks for the Structural Analysis and Monitoring of Railway Bridges: A Systematic Review," Mathematics, MDPI, vol. 13(10), pages 1-40, May.

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