Physics-informed multi-fidelity surrogate modeling of fluid flow in porous media

Predicting the behavior of a fluid as it flows through porous media is critical for electrochemical devices and other scientific, industrial, and environmental applications. The main challenge lies in accurately capturing the complex, multi-scale fluid flow behavior through irregular porous microstructures, all while maintaining computational efficiency. In this paper, we introduce a multi-fidelity surrogate model that predicts the high-fidelity flow field state variables in explicit porous media microstructures with minimal computational cost. Our approach begins by collecting both low-fidelity and high-fidelity simulation data to train the surrogate model. The former low-fidelity data are obtained from numerical simulations of fluid flowing through macro-scale structures having homogenized effective material properties. On the other hand, the latter high-fidelity data include geometric details of the dehomogenized explicit porous media microstructure. This technique combines the detailed accuracy of high-fidelity data with the computational efficiency of low-fidelity data, thus enhancing the model performance. In addition, we integrate physics-informed neural networks into the surrogate modeling process, embedding physical laws derived from the Navier–Stokes equations that govern fluid flow. This multi-scale, multi-fidelity approach offers a precise and cost-effective solution for predicting the fluid flow velocity and pressure fields in the porous media. For relevant porous media fluid flow applications, we show a ∼103× faster solution in terms of increased computational speed for a given model with reasonable representative accuracy of the solution, within a range of ∼5%–20% for velocity and ≤10% for pressure fields.