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In recent years, convolutional neural networks (CNNs) have experienced an increasing interest for their ability to perform fast approximation of effective hydrodynamic parameters in porous media research and applications. This paper presents a novel methodology for permeability prediction from micro-CT scans of geological rock samples. The training data set for CNNs dedicated to permeability prediction consists of permeability labels that are typically generated by classical lattice Boltzmann methods (LBM) that simulate the flow through the pore space of the segmented image data. We instead perform direct numerical simulation (DNS) by solving the stationary Stokes equation in an efficient and distributed-parallel manner. As such, we circumvent the convergence issues of LBM that frequently are observed on complex pore geometries, and therefore, improve on the generality and accuracy of our training data set. Using the DNS-computed permeabilities, a physics-informed CNN PhyCNN) is trained by additionally providing a tailored characteristic quantity of the pore space. More precisely, by exploiting the connection to flow problems on a graph representation of the pore space, additional information about confined structures is provided to the network in terms of the maximum flow value, which is the key innovative component of our workflow. As a result, unprecedented prediction accuracy and robustness are observed for a variety of sandstone samples from archetypal rock formations.
Physics Informed Neural Network (PINN) is a scientific computing framework used to solve both forward and inverse problems modeled by Partial Differential Equations (PDEs). This paper introduces IDRLnet, a Python toolbox for modeling and solving prob
Failure trajectories, identifying the probable failure zones, and damage statistics are some of the key quantities of relevance in brittle fracture applications. High-fidelity numerical solvers that reliably estimate these relevant quantities exist b
Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high nonlinearit
We introduce in this work the normalizing field flows (NFF) for learning random fields from scattered measurements. More precisely, we construct a bijective transformation (a normalizing flow characterizing by neural networks) between a Gaussian rand
We introduce the concept of a Graph-Informed Neural Network (GINN), a hybrid approach combining deep learning with probabilistic graphical models (PGMs) that acts as a surrogate for physics-based representations of multiscale and multiphysics systems