Florian Frank

Florian Frank, Chen Liu, Faruk O. Alpak et al.

A numerical method is formulated for the solution of the advective Cahn-Hilliard (CH) equation with constant and degenerate mobility in three-dimensional porous media with non-vanishing velocity on the exterior boundary. The CH equation describes phase separation of an immiscible binary mixture at constant temperature in the presence of a mass constraint and dissipation of free energy. Porous media/pore-scale problems specifically entail high-resolution images of rocks in which the solid matrix and pore spaces are fully resolved. The interior penalty discontinuous Galerkin method is used for the spatial discretization of the CH equation in mixed form, while a semi-implicit convex-concave splitting is utilized for temporal discretization. The spatial approximation order is arbitrary, while it reduces to a finite volume scheme for the choice of elementwise constants. The resulting nonlinear systems of equations are reduced using the Schur complement and solved via Newton's method. The numerical scheme is first validated using numerical convergence tests and then applied to a number of fundamental problems for validation and numerical experimentation purposes including the case of degenerate mobility. First-order physical applicability and robustness of the numerical method are shown in a breakthrough scenario on a voxel set obtained from a micro-CT scan of a real sandstone rock sample.

Stephan Gärttner, Florian Frank, Fabian Woller et al.

In the past several years, convolutional neural networks (CNNs) have proven their capability to predict characteristic quantities in porous media research directly from pore-space geometries. Due to the frequently observed significant reduction in computation time in comparison to classical computational methods, bulk parameter prediction via CNNs is especially compelling, e.g. for effective diffusion. While the current literature is mainly focused on fully saturated porous media, the partially saturated case is also of high interest. Due to the qualitatively different and more complex geometries of the domain available for diffusive transport present in this case, standard CNNs tend to lose robustness and accuracy with lower saturation rates. In this paper, we demonstrate the ability of CNNs to perform predictions of relative diffusion directly from full pore-space geometries. As such, our CNN conveniently fuses diffusion prediction and a well-established morphological model which describes phase distributions in partially saturated porous media.

Florian Frank, Stefan Milius, Jurriaan Rot et al.

Automata over infinite alphabets have emerged as a convenient computational model for processing structures involving data, such as nonces in cryptographic protocols or data values in XML documents. We introduce active learning methods for bar automata, a species of automata that process finite data words represented as bar strings, which are words with explicit name binding letters. Bar automata have pleasant algorithmic properties. We develop a framework in which every learning algorithm for standard deterministic or nondeterministic finite automata over finite alphabets can be used to learn bar automata, with a query complexity determined by that of the chosen learner. The technical key to our approach is the algorithmic handling of $α$-equivalence of bar strings, which allows bridging the gap between finite and infinite alphabets. The principles underlying our framework are generic and also apply to bar Büchi automata and bar tree automata, leading to the first active learning methods for data languages of infinite words and finite trees.

Stephan Gärttner, Faruk O. Alpak, Andreas Meier et al.

In recent years, convolutional neural networks (CNNs) have experienced an increasing interest in their ability to perform a 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 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. The robustness of this approach is reflected by very high prediction accuracy, which is observed for a variety of sandstone samples from archetypal rock formations.

Max Grossman, Christopher Thiele, Mauricio Araya-Polo et al.

We contribute a third-party survey of sparse matrix-vector (SpMV) product performance on industrial-strength, large matrices using: (1) The SpMV implementations in Intel MKL, the Trilinos project (Tpetra subpackage), the CUSPARSE library, and the CUSP library, each running on modern architectures. (2) NVIDIA GPUs and Intel multi-core CPUs (supported by each software package). (3) The CSR, BSR, COO, HYB, and ELL matrix formats (supported by each software package).