 Investigating neural networks with groundwater flow equation lossVincenzo Schiano Di Cola, Vittorio Bauduin, Marco Berardi, Filippo Notarnicola and Salvatore Cuomo Mathematics and Computers in Simulation (MATCOM), 2025, vol. 230, issue C, 80-93 Abstract: Physics-Informed Neural Networks (PINNs) are considered a powerful tool for solving partial differential equations (PDEs), particularly for the groundwater flow (GF) problem. In this paper, we investigate how the deep learning (DL) architecture, within the PINN framework, is connected to the ability to compute a more or less accurate numerical GF solution, so the link ‘PINN architecture - numerical performance’ is explored. Specifically, this paper explores the effect of various DL components, such as different activation functions and neural network structures, on the computational framework. Through numerical results and on the basis of some theoretical foundations of PINNs, this research aims to improve the explicability of PINNs to resolve, in this case, the one-dimensional GF equation. Moreover, our problem involves source terms described by a Dirac delta function, providing insights into the role of DL architecture in solving complex PDEs. Keywords: Groundwater flow; Physics-Informed Neural Networks (PINNs); Neural network optimization (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:230:y:2025:i:c:p:80-93 DOI: 10.1016/j.matcom.2024.10.039 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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