Non-Intrusive Reduced Order Modeling Applied to Fluid Flow in Fractured Porous Media using Neural Networks

The simulation of the fluid flow in fractured porous media has various applications - from subsurface to biological processes - and has been the focus of several works over the last decade. The mathematical description of the problem and its solution is challenging since the domain is generally anisotropic, heterogeneous, and has substantially discontinuous material properties that can span several magnitude orders. In this work, we apply a non-intrusive proper orthogonal decomposition-based reduced order model (POD-ROM) for the steady-state fluid flow problem in a fractured porous medium. Two fluid flow models are used for discrete fractures: an equidimensional model, in which both porous matrix and fracture are modeled as d-dimensional entities, and a mixed-dimensional model, in which the fracture is modeled as a (d−1)-dimensional entity. These models are solved using the mixed finite element method with the lowest order Raviart-Thomas elements. Reduced bases are then extracted through the POD for both velocity and pressure components. Subsequently, artificial neural networks are used to approximate the coefficients corresponding to each reduced basis. The main objective of this work is to provide a cheap framework, in terms of CPU and memory requirements, for the solution of fluid flow problems in fractured porous media with reasonable accuracy.