<p>Modeling nonlinear multiphysics transport phenomena in porous media particularly under the coupled influence of thermal radiation, magnetic fields, and bioconvection poses significant challenges for traditional numerical solvers due to the computational burden and the complexity of handling strongly coupled PDE systems. This study presents two AI-driven deep learning frameworks, Unified Physics-Informed Neural Networks (UPINN) and Modular Physics-Informed Neural Networks (MPINN), for simulating buoyancy-influenced heat, mass, and microorganism transport in a Darcy–Forchheimer porous medium. UPINN employs a single network to learn all solution fields simultaneously, while MPINN assigns dedicated subnetworks to each physical variable, improving stability, convergence, and scalability. By embedding the non-dimensionalized governing equations into the loss function, both approaches enable unsupervised learning without labeled data. Comparative analysis shows that UPINN provides computational simplicity and faster training, whereas MPINN achieves higher accuracy and better resolution of localized boundary-layer features. Performance evaluation under varying neural architectures, learning rates, and collocation point distributions confirms the robustness of both frameworks. Validation against finite difference method (FDM) solutions demonstrates close agreement, with MPINN delivering superior precision in capturing sharp gradients. Parametric investigations further quantify the influence of physical parameters on local Nusselt, Sherwood, and microorganism density distributions. These findings establish UPINN and MPINN as reliable, data-efficient AI surrogates for complex multiphysics transport in porous media, with MPINN exhibiting enhanced accuracy and generalization capabilities in challenging nonlinear regimes.</p>

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AI-driven unified and modular PINN frameworks for multiphysics convection in porous media

  • S. Sarthak,
  • D. Srinivasacharya

摘要

Modeling nonlinear multiphysics transport phenomena in porous media particularly under the coupled influence of thermal radiation, magnetic fields, and bioconvection poses significant challenges for traditional numerical solvers due to the computational burden and the complexity of handling strongly coupled PDE systems. This study presents two AI-driven deep learning frameworks, Unified Physics-Informed Neural Networks (UPINN) and Modular Physics-Informed Neural Networks (MPINN), for simulating buoyancy-influenced heat, mass, and microorganism transport in a Darcy–Forchheimer porous medium. UPINN employs a single network to learn all solution fields simultaneously, while MPINN assigns dedicated subnetworks to each physical variable, improving stability, convergence, and scalability. By embedding the non-dimensionalized governing equations into the loss function, both approaches enable unsupervised learning without labeled data. Comparative analysis shows that UPINN provides computational simplicity and faster training, whereas MPINN achieves higher accuracy and better resolution of localized boundary-layer features. Performance evaluation under varying neural architectures, learning rates, and collocation point distributions confirms the robustness of both frameworks. Validation against finite difference method (FDM) solutions demonstrates close agreement, with MPINN delivering superior precision in capturing sharp gradients. Parametric investigations further quantify the influence of physical parameters on local Nusselt, Sherwood, and microorganism density distributions. These findings establish UPINN and MPINN as reliable, data-efficient AI surrogates for complex multiphysics transport in porous media, with MPINN exhibiting enhanced accuracy and generalization capabilities in challenging nonlinear regimes.