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

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

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 230, issue C, 541-558

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.

Keywords: Deep artificial neural networks; Scientific machine learning; Time discrete PINNs; Implicit Euler and Crank–Nicolson methods; Stiff problems; Nonlinear sustainability PDE model; Dye-sensitized solar cells (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:230:y:2025:i:c:p:541-558

DOI: 10.1016/j.matcom.2024.10.043

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