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<p>This study presents an application of Physics-Informed Neural Networks (PINNs) and Galerkin Physics-Informed Neural Networks (G-PINNs) to the modeling of tracer dispersion in porous media using experimental data from sodium chloride transport in Berea sandstone cores. The proposed framework considers Dirichlet and Neumann boundary conditions in a 1D cylindrical coordinate system and employs artificial neural networks as basis functions in the G-PINN formulation to improve numerical accuracy. Both methodologies are trained to satisfy the underlying advection-diffusion equation while fitting the available experimental measurements. The study includes direct and inverse problem applications, with particular emphasis on estimating the effective tracer dispersion coefficient from outlet concentration data. To improve convergence in the inverse problem, a modified optimization strategy combining a scaled L-BFGS scheme and a reduced number of Adam iterations is introduced. The results show that both PINN and G-PINN can reproduce the concentration evolution with good agreement, while the proposed scaled L-BFGS + Adam strategy significantly reduces computational time compared with using Adam alone. These findings highlight the potential of PINN-based and Galerkin-based neural formulations for experimental-data-driven modeling and parameter estimation in porous media transport problems, with applications in reservoir engineering, contaminant transport, and related subsurface flow systems.</p>

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Galerkin physics-informed neural network approach for inverse problems. Application to estimation of tracer dispersion in porous media

  • 期刊论文

  • 发表日期：

    2026年4月30日

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  • Luis Constante,
  • Adolfo Pires,
  • Martín A. Díaz-Viera

摘要

This study presents an application of Physics-Informed Neural Networks (PINNs) and Galerkin Physics-Informed Neural Networks (G-PINNs) to the modeling of tracer dispersion in porous media using experimental data from sodium chloride transport in Berea sandstone cores. The proposed framework considers Dirichlet and Neumann boundary conditions in a 1D cylindrical coordinate system and employs artificial neural networks as basis functions in the G-PINN formulation to improve numerical accuracy. Both methodologies are trained to satisfy the underlying advection-diffusion equation while fitting the available experimental measurements. The study includes direct and inverse problem applications, with particular emphasis on estimating the effective tracer dispersion coefficient from outlet concentration data. To improve convergence in the inverse problem, a modified optimization strategy combining a scaled L-BFGS scheme and a reduced number of Adam iterations is introduced. The results show that both PINN and G-PINN can reproduce the concentration evolution with good agreement, while the proposed scaled L-BFGS + Adam strategy significantly reduces computational time compared with using Adam alone. These findings highlight the potential of PINN-based and Galerkin-based neural formulations for experimental-data-driven modeling and parameter estimation in porous media transport problems, with applications in reservoir engineering, contaminant transport, and related subsurface flow systems.