Geometry Enhanced Generative Adversarial Networks for Random Heterogeneous Material Representation

The representation of material structure geometry is essential to the reconstruction, physical simulation, and the multiscale structure design with Random Heterogeneous Material (RHM). Traditional approaches to material structure representation often need to balance the trade-off between efficacy and accuracy. Recently, deep learning-based techniques have been adopted to reduce the computational time of RHM reconstruction. However, existing approaches generally lack guarantees over key RHM characteristics, including Minkowski functionals and correlation functions. We propose a novel approach to geometrically enhancing the deep learning-based RHM representation by introducing Minkowski functionals, a set of topological and geometrical characteristics of material structure, into the training of conditional Generative Adversarial Networks (cGAN). This hybrid approach combines the feature learning capability of deep learning with the well-established material structure characteristics, greatly improving the accuracy of the RHM representation while maintaining its efficiency. The effectiveness of the proposed hybrid approach is validated through the reconstruction of a wide range of natural and manmade materials, including Voronoi foam structures, femur, and sandstone. Through computational experiments, we demonstrate that geometrically enhancing the training of cGAN for RHM representation not only significantly decreases the representation error in Minkowski functionals between input sample materials and reconstructed results, but also improves the performance of other material structure characteristics, such as two-point correlation functions.

The Effect of Topology on Phase Behavior under Confinement

This work studies how morphology (i.e., the shape of a structure) and topology (i.e., how different structures are connected) influence wall adsorption and capillary condensation under tight confinement. Numerical simulations based on classical density functional theory (cDFT) are run for a wide variety of geometries using both hard-sphere and Lennard-Jones fluids. These cDFT computations are compared to results obtained using the Minkowski functionals. It is found that the Minkowski functionals can provide a good description of the behavior of Lennard-Jones fluids down to small system sizes. In addition, through decomposition of the free energy, the Minkowski functionals provide a good framework to better understand what are the dominant contributions to the phase behavior of a system. Lastly, while studying the phase envelope shift as a function of the Minkowski functionals it is found that topology has a different effect depending on whether the phase transition under consideration is a continuous or a discrete (first-order) transition.

Local Measures Distribution for the Estimation of the Elongation Ratio of the Typical Grain in Homogeneous Boolean Models

We introduce a particular localization of the Minkowski functionals to characterize and discriminate different random spatial structures. The aim of this paper is to present a method estimating the typical grain elongation ratio in a homogeneous Boolean model. The use of this method is demonstrated on a range of Boolean models of rectangles featuring fixed and random elongation ratio. An optimization algorithm is performed to determine the elongation ratio which maximize the likelihood function of the probability density associated with the local perimeter measure. Therefore, the elongation ratio of the typical grain can be deduced.

Histological classification of non-small cell lung cancer using Gabor filtering Minkowski functionals and Neighborhood Component Analysis on CT images.

Information regarding the histological types of non-small cell lung cancer is essential to determine the treatment strategy. Although several radiomics studies using almost similar feature variables were reported, a considerable variation in the performances has been observed. In this study, as novel radiomic features, 2D Gabor filtering Minkowski functionals were used. They were calculated in rotational invariant and both scale and rotational invariant ways using circular shift operations of Gabor filters on nonenhanced computed tomographic images. Eighty-six patients (47 adenocarcinomas, 39 squamous cell carcinomas) were analyzed. Two independent observers manually delineated a single slice segmentation of a tumor. Feature selection was made by neighborhood component analysis. Among various classifiers, 1-nearest neighbor gave a promising performance. The observer-averaged accuracy of rotational invariant analysis was 86.28% and that of both scale and rotational invariant one was 88.27%. However, there was no common feature among the ten top-ranked features of each observer with the identical Gabor filtering type. Hence further study of the robustness is necessary to create a more reliable model.

Morphology of relaxed and merging galaxy clusters: analytical models for monolithic Minkowski functionals

ABSTRACT Galaxy clusters exhibit a rich morphology during the early and intermediate stages of mass assembly, especially beyond their boundary. A classification scheme based on shapefinders deduced from the Minkowski functionals is examined to fully account for the morphological diversity of galaxy clusters, including relaxed and merging clusters, clusters fed by filamentary structures, and cluster-pair bridges. These configurations are conveniently treated with idealized geometric models and analytical formulas, some of which are novel. Examples from CLASH and LC2 clusters and observed cluster-pair bridges are discussed.

Machine Learning Real Space Microstructure Characteristics from Scattering Data

Using tools from morphological image analysis, we characterise spinodal decomposition microstructures by their Minkowski functionals, and search for a correlation between them and data from scattering experiments. To do this,...