Equivariant geometric learning for digital rock physics: estimating formation factor and effective permeability tensors from Morse graph

We present a SE(3)-equivariant graph neural network (GNN) approach that directly predicting the formation factor and effective permeability from micro-CT images. FFT solvers are established to compute both the formation factor and effective permeability, while the topology and geometry of the pore space are represented by a persistence-based Morse graph. Together, they constitute the database for training, validating, and testing the neural networks. While the graph and Euclidean convolutional approaches both employ neural networks to generate low-dimensional latent space to represent the features of the micro-structures for forward predictions, the SE(3) equivariant neural network is found to generate more accurate predictions, especially when the training data is limited. Numerical experiments have also shown that the new SE(3) approach leads to predictions that fulfill the material frame indifference whereas the predictions from classical convolutional neural networks (CNN) may suffer from spurious dependence on the coordinate system of the training data. Comparisons among predictions inferred from training the CNN and those from graph convolutional neural networks (GNN) with and without the equivariant constraint indicate that the equivariant graph neural network seems to perform better than the CNN and GNN without enforcing equivariant constraints

Big-Data Science in Porous Materials: Materials Genomics and Machine Learning

By combining metal nodes with organic linkers we can potentially synthesize millions of possible metal organic frameworks (MOFs). At present, we have libraries of over ten thousand synthesized materials and millions of in-silico predicted materials. The fact that we have so many materials opens many exciting avenues to tailor make a material that is optimal for a given application. However, from an experimental and computational point of view we simply have too many materials to screen using brute-force techniques. In this review, we show that having so many materials allows us to use big-data methods as a powerful technique to study these materials and to discover complex correlations. The first part of the review gives an introduction to the principles of big-data science. We emphasize the importance of data collection, methods to augment small data sets, how to select appropriate training sets. An important part of this review are the different approaches that are used to represent these materials in feature space. The review also includes a general overview of the different ML techniques, but as most applications in porous materials use supervised ML our review is focused on the different approaches for supervised ML. In particular, we review the different method to optimize the ML process and how to quantify the performance of the different methods. In the second part, we review how the different approaches of ML have been applied to porous materials. In particular, we discuss applications in the field of gas storage and separation, the stability of these materials, their electronic properties, and their synthesis. The range of topics illustrates the large variety of topics that can be studied with big-data science. Given the increasing interest of the scientific community in ML, we expect this list to rapidly expand in the coming years.Comment: Editorial changes (typos fixed, minor adjustments to figures

High-Throughput Screening Approach for Nanoporous Materials Genome Using Topological Data Analysis: Application to Zeolites

The materials genome initiative has led to the creation of a large (over a million) database of different classes of nanoporous materials. As the number of hypothetical materials that can, in principle, be experimentally synthesized is infinite, a bottleneck in the use of these databases for the discovery of novel materials is the lack of efficient computational tools to analyze them. Current approaches use brute-force molecular simulations to generate thermodynamic data needed to predict the performance of these materials in different applications, but this approach is limited to the analysis of tens of thousands of structures due to computational intractability. As such, it is conceivable and even likely that the best nanoporous materials for any given application have yet to be discovered both experimentally and theoretically. In this article, we seek a computational approach to tackle this issue by transitioning away from brute-force characterization to high-throughput screening methods based on big-data analysis, using the zeolite database as an example. For identifying and comparing zeolites, we used a topological data analysis-based descriptor (TD) recognizing pore shapes. For methane storage and carbon capture applications, our analyses seeking pairs of highly similar zeolites discovered good correlations between performance properties of a seed zeolite and the corresponding pair, which demonstrates the capability of TD to predict performance properties. It was also shown that when some top zeolites are known, TD can be used to detect other high-performing materials as their neighbors with high probability. Finally, we performed high-throughput screening of zeolites based on TD. For methane storage (or carbon capture) applications, the promising sets from our screenings contained high-percentages of top-performing zeolites: 45% (or 23%) of the top 1% zeolites in the entire set. This result shows that our screening approach using TD is highly efficient in finding high-performing materials. We expect that this approach could easily be extended to other applications by simply adjusting one parameter, the size of the target gas molecule

Materials fatigue prediction using graph neural networks on microstructure representations

The local prediction of fatigue damage within polycrystals in a high-cycle fatigue setting is a long-lasting and challenging task. It requires identifying grains tending to accumulate plastic deformation under cyclic loading. We address this task by transcribing ferritic steel microtexture and damage maps from experiments into a microstructure graph. Here, grains constitute graph nodes connected by edges whenever grains share a common boundary. Fatigue loading causes some grains to develop slip markings, which can evolve into microcracks and lead to failure. This data set enables applying graph neural network variants on the task of binary grain-wise damage classification. The objective is to identify suitable data representations and models with an appropriate inductive bias to learn the underlying damage formation causes. Here, graph convolutional networks yielded the best performance with a balanced accuracy of 0.72 and a F$_1$-score of 0.34, outperforming phenomenological crystal plasticity (+ 68%) and conventional machine learning (+ 17%) models by large margins. Further, we present an interpretability analysis that highlights the grains along with features that are considered important by the graph model for the prediction of fatigue damage initiation, thus demonstrating the potential of such techniques to reveal underlying mechanisms and microstructural driving forces in critical grain ensembles

Contour tree connectivity and analysis of microstructures

The connectivity of microstructures is directly related to the physical properties of materials. Currently, the Euler number is the most popular measure of connectivity. It is an elegant topological invariant, however, it does not provide information about cavities or the proximities and sizes of objects. In this thesis, an alternative measure called contour tree connectivity (CTC) is developed and its applications for the analysis of microstructures are studied. CTC is derived from contour trees that are used in the first publication to represent complex binary images with simple graphs. By analyzing contour trees, CTC produces new connectivity information that is not provided by other approaches described in the literature. Contour tree representation of binary images and CTC can be computed for any dimensions of data and topology as explained in the second publication. Moreover, CTC is designed to be a scalar between 0 and 1, which makes it easy to use and understand. In this thesis, the use of CTC for analyzing microstructures is presented in two studies. In the first study, the microstructure of trabecular bone is analyzed in relation to its mechanical strength. In the second study, the relationship between microstructures and the fluid flow within materials are examined. The results from these studies show that CTC contributes to the understanding of how the structural properties of materials are linked to their physical properties. To conclude, with its unique properties, CTC complements the structural information provided by currently used measures. This makes it an important image analysis tool for the study of the microstructures of materials such as soil, paper, filters and food products as well as biomaterials and biological tissues

Data-Augmented Structure-Property Mapping for Accelerating Computational Design of Advanced Material Systems

abstract: Advanced material systems refer to materials that are comprised of multiple traditional constituents but complex microstructure morphologies, which lead to their superior properties over conventional materials. This dissertation is motivated by the grand challenge in accelerating the design of advanced material systems through systematic optimization with respect to material microstructures or processing settings. While optimization techniques have mature applications to a large range of engineering systems, their application to material design meets unique challenges due to the high dimensionality of microstructures and the high costs in computing process-structure-property (PSP) mappings. The key to addressing these challenges is the learning of material representations and predictive PSP mappings while managing a small data acquisition budget. This dissertation thus focuses on developing learning mechanisms that leverage context-specific meta-data and physics-based theories. Two research tasks will be conducted: In the first, we develop a statistical generative model that learns to characterize high-dimensional microstructure samples using low-dimensional features. We improve the data efficiency of a variational autoencoder by introducing a morphology loss to the training. We demonstrate that the resultant microstructure generator is morphology-aware when trained on a small set of material samples, and can effectively constrain the microstructure space during material design. In the second task, we investigate an active learning mechanism where new samples are acquired based on their violation to a theory-driven constraint on the physics-based model. We demonstrate using a topology optimization case that while data acquisition through the physics-based model is often expensive (e.g., obtaining microstructures through simulation or optimization processes), the evaluation of the constraint can be far more affordable (e.g., checking whether a solution is optimal or equilibrium). We show that this theory-driven learning algorithm can lead to much improved learning efficiency and generalization performance when such constraints can be derived. The outcomes of this research is a better understanding of how physics knowledge about material systems can be integrated into machine learning frameworks, in order to achieve more cost-effective and reliable learning of material representations and predictive models, which are essential to accelerate computational material design.Dissertation/ThesisDoctoral Dissertation Mechanical Engineering 201

Automated Discovery of porous molecular materials facilitated by characterization of molecular porosity

Porous materials are critical to many industrial sectors, including petrochemicals, energy and water. Traditional porous polymers and zeolites are currently most widely employed within membranes, as adsorbents for separations and storage, and as heterogeneous catalysts. The emerging advanced porous materials, e.g. extended framework materials and molecular porous materials, can boost performance and energy-efficiency of the current technologies because of the unprecedented level of control of their structure and function. The enormous possibilities for tuning these materials by changing their building blocks mean that, in principle, optimally performing materials for a variety of applications can be systematically designed. However, the process of finding a set of optimal structures for a given application could take decades using the traditional materials development approaches. These is a substantial payoff for developing tools and approaches that can accelerate this process. Among advanced porous materials, porous molecular materials are one of the most recent members though they have already attracted significant interest......Programa de Doctorado en Ciencia e Ingeniería de Materiales por la Universidad Carlos III de MadridPresidente: Germán Ignacio Sastre Navarro.- Secretario: Javier Carrasco Rodríguez.- Vocal: Andreas Mavrantonaki