Physics informed neural networks for solving highly anisotropic diffusion equations

W. Zhang, W. Diab, M. Al Kobaisi

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    2 Scopus citations

    Abstract

    In recent years, Physics Informed Neural Networks (PINNs) have generated considerable interest in the scientific computing community as an alternative, or potential contender, to traditional numerical discretization methods such as finite- difference, volume, and element methods, for solving partial differential equations (PDE). In PINNs, the governing equations are incorporated into a loss function as a regularization term to guide the neural network so that the solution respects the underlying physics, hence the name ‘physics informed’. In this work, we investigate the performance of PINNs in solving the highly anisotropic diffusion equation that models fluid flow in subsurface porous media. Several levels of permeability anisotropy are tested. The results show that PINNs have excellent performance when the solution is smooth regardless of the strength of permeability anisotropy. However, PINNs struggle to give adequate results when the solution has large gradients, for example, when the solution is induced by a concentrated source term. The problem is exacerbated by higher levels of permeability anisotropy. Our results highlight a few limitations in the current implementation of physics-informed neural networks for fluid flow in porous media and show that we still have ways to go before it can compete with traditional numerical methods.

    Original languageBritish English
    Title of host publicationEuropean Conference on the Mathematics of Geological Reservoirs 2022, ECMOR 2022
    ISBN (Electronic)9789462824263
    DOIs
    StatePublished - 2022
    EventEuropean Conference on the Mathematics of Geological Reservoirs 2022, ECMOR 2022 - The Hague, Virtual, Netherlands
    Duration: 5 Sep 20227 Sep 2022

    Publication series

    NameEuropean Conference on the Mathematics of Geological Reservoirs 2022, ECMOR 2022

    Conference

    ConferenceEuropean Conference on the Mathematics of Geological Reservoirs 2022, ECMOR 2022
    Country/TerritoryNetherlands
    CityThe Hague, Virtual
    Period5/09/227/09/22

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