A surrogate model for the prediction of permeabilities and flow through porous media

Abstract

In this contribution we present an approach to generate a data driven surrogate model for the prediction of permeabilities and flow through two dimensional random micro-heterogeneous materials. The laminar flow is well described by Darcy's law. In order to achieve an efficient computational tool for the generation of the database (up to 10 3 realizations), needed for the training of the neural networks, we apply a stochastic model based on the Brownian motion. The stationary state of the resulting stochastic model solves the Darcy equation and can be iteratively solved by a Monte Carlo approach applied to a particle simulation. Improved numerical efficiency can be yield by usage of the related transition matrix.

A data generation approach for surrogate models for magneto‐static simulations

“…From various successful applications of deep learning, it is clear that this method is applicable in a wide range of different disciplines. The approach described in this contribution is a generalization of the work in [3,4] allowing arbitrary permeabilities not restricted to 0 or 1. As a model system, we have chosen here the stationary magnetic stray field arising if a constant magnetic field is applied to an inhomogeneous magnetic material.…”