Machine Learning in Heterogeneous Porous Materials

The "Workshop on Machine learning in heterogeneous porous materials" brought together international scientific communities of applied mathematics, porous media, and material sciences with experts in the areas of heterogeneous materials, machine learning (ML) and applied mathematics to identify how ML can advance materials research. Within the scope of ML and materials research, the goal of the workshop was to discuss the state-of-the-art in each community, promote crosstalk and accelerate multi-disciplinary collaborative research, and identify challenges and opportunities. As the end result, four topic areas were identified: ML in predicting materials properties, and discovery and design of novel materials, ML in porous and fractured media and time-dependent phenomena, Multi-scale modeling in heterogeneous porous materials via ML, and Discovery of materials constitutive laws and new governing equations. This workshop was part of the AmeriMech Symposium series sponsored by the National Academies of Sciences, Engineering and Medicine and the U.S. National Committee on Theoretical and Applied Mechanics.

Multi-Scale Neural Networks for to Fluid Flow in 3D Porous Media

The permeability of complex porous materials can be obtained via direct flow simulation, which provides the most accurate results, but is very computationally expensive. In particular, the simulation convergence time scales poorly as simulation domains become tighter or more heterogeneous. Semi-analytical models that rely on averaged structural properties (i.e. porosity and tortuosity) have been proposed, but these features only summarize the domain, resulting in limited applicability. On the other hand, data-driven machine learning approaches have shown great promise for building more general models by virtue of accounting for the spatial arrangement of the domains solid boundaries. However, prior approaches building on the Convolutional Neural Network (ConvNet) literature concerning 2D image recognition problems do not scale well to the large 3D domains required to obtain a Representative Elementary Volume (REV). As such, most prior work focused on homogeneous samples, where a small REV entails that that the global nature of fluid flow could be mostly neglected, and accordingly, the memory bottleneck of addressing 3D domains with ConvNets was side-stepped. Therefore, important geometries such as fractures and vuggy domains could not be well-modeled. In this work, we address this limitation with a general multiscale deep learning model that is able to learn from porous media simulation data. By using a coupled set of neural networks that view the domain on different scales, we enable the evaluation of large images in approximately one second on a single Graphics Processing Unit. This model architecture opens up the possibility of modeling domain sizes that would not be feasible using traditional direct simulation tools on a desktop computer.

MudrockNet: Semantic Segmentation of Mudrock SEM Images through Deep Learning

Segmentation and analysis of individual pores and grains of mudrocks from scanning electron microscope images is non-trivial because of noise, imaging artifacts, variation in pixel grayscale values across images, and overlaps in grayscale values among different physical features such as silt grains, clay grains, and pores in an image, which make their identification difficult. Moreover, because grains and pores often have overlapping grayscale values, direct application of threshold-based segmentation techniques is not sufficient. Recent advances in the field of computer vision have made it easier and faster to segment images and identify multiple occurrences of such features in an image, provided that ground-truth data for training the algorithm is available. Here, we propose a deep learning SEM image segmentation model, MudrockNet based on Google's DeepLab-v3+ architecture implemented with the TensorFlow library. The ground-truth data was obtained from an image-processing workflow applied to scanning electron microscope images of uncemented muds from the Kumano Basin offshore Japan at depths < 1.1 km. The trained deep learning model obtained a pixel-accuracy about 90%, and predictions for the test data obtained a mean intersection over union (IoU) of 0.6591 for silt grains and 0.6642 for pores. We also compared our model with the random forest classifier using trainable Weka segmentation in ImageJ, and it was observed that MudrockNet gave better predictions for both silt grains and pores. The size, concentration, and spatial arrangement of the silt and clay grains can affect the petrophysical properties of a mudrock, and an automated method to accurately identify the different grains and pores in mudrocks can help improve reservoir and seal characterization for petroleum exploration and anthropogenic waste sequestration.

Modeling nanoconfinement effects using active learning

Predicting the spatial configuration of gas molecules in nanopores of shale formations is crucial for fluid flow forecasting and hydrocarbon reserves estimation. The key challenge in these tight formations is that the majority of the pore sizes are less than 50 nm. At this scale, the fluid properties are affected by nanoconfinement effects due to the increased fluid-solid interactions. For instance, gas adsorption to the pore walls could account for up to 85% of the total hydrocarbon volume in a tight reservoir. Although there are analytical solutions that describe this phenomenon for simple geometries, they are not suitable for describing realistic pores, where surface roughness and geometric anisotropy play important roles. To describe these, molecular dynamics (MD) simulations are used since they consider fluid-solid and fluid-fluid interactions at the molecular level. However, MD simulations are computationally expensive, and are not able to simulate scales larger than a few connected nanopores. We present a method for building and training physics-based deep learning surrogate models to carry out fast and accurate predictions of molecular configurations of gas inside nanopores. Since training deep learning models requires extensive databases that are computationally expensive to create, we employ active learning (AL). AL reduces the overhead of creating comprehensive sets of high-fidelity data by determining where the model uncertainty is greatest, and running simulations on the fly to minimize it. The proposed workflow enables nanoconfinement effects to be rigorously considered at the mesoscale where complex connected sets of nanopores control key applications such as hydrocarbon recovery and CO2 sequestration.