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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. 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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