Topological Analysis of Solid Oxide Cell Electrodes Based on Persistent Homology

Solid oxide cells (SOCs) have been attracting significant interest for their potential in effective energy utilization, and optimization of their electrode microstructures is strongly demanded for enhanced performance. Data‐driven approaches for computationally generating and evaluating artificial microstructures are expected to accelerate the discovery of optimal porous structures. In this study, a machine learning model based on generative adversarial networks (GANs) is developed to generate artificial porous microstructures of SOC hydrogen electrodes while precisely controlling two key structural characteristics: volume fraction and specific surface area. The generator receives a conditional vector comprising the values of volume fractions and specific surface areas, which is concatenated with a latent vector. After training on real microstructure datasets, the model successfully generates artificial structures that are visually indistinguishable from real ones, free from unnatural artifacts, and statistically consistent with the real structures. Furthermore, persistent homology analysis is employed to assess the similarity between the real and artificial structures by uncovering hidden topological characteristics of the structures. The results demonstrate that the developed GAN model captures not only explicit statistical characteristics but also implicit, nonintuitive topological characteristics of porous electrode microstructures.

Results from a series of two‐phase fluid flow experiments in Leopard, Berea, and Bentheimer sandstones are presented. Fluid configurations are characterized using laboratory‐based and synchrotron based 3‐D X‐ray computed tomography. All flow experiments are conducted under capillary‐dominated conditions. We conduct geometry‐topology analysis via persistent homology and compare this to standard topological and watershed‐partition‐based pore‐network statistics. Metrics identified as predictors of nonwetting fluid trapping are calculated from the different analytical methods and are compared to levels of trapping measured during drainage‐imbibition cycles in the experiments. Metrics calculated from pore networks (i.e., pore body‐throat aspect ratio and coordination number) and topological analysis (Euler characteristic) do not correlate well with trapping in these samples. In contrast, a new metric derived from the persistent homology analysis, which incorporates counts of topological features as well as their length scale and spatial distribution, correlates very well (R2 = 0.97) to trapping for all systems. This correlation encompasses a wide range of porous media and initial fluid configurations, and also applies to data sets of different imaging and image processing protocols.

Gadolinium doped ceria (GDC) gains increasing attention as a promising material for both solid oxide fuel cells (SOFCs) and solid oxide electrolysis cells (SOECs). The GDC-based electrodes demonstrate positive features, e.g. enhanced electrochemical performance in low operation temperatures, resistivity to sulfur poisoning and carbon deposition, etc. As GDC is a mixed electronic-ionic conductor in reducing atmosphere, electrochemical reactions can be supported by the double phase boundary (DPB) at the GDC surface. Several studies demonstrated that the DPB reaction may dominate the electrochemical performance over triple phase boundary (TPB) reaction in Ni-GDC electrodes, where it can account for as much as 95 % of the total reaction depending on the cermet microstructure [1]. Recent studies even show that pure ceria electrodes can achieve substantial power density [2,3]. In this context, the microstructure design principle for GDC-based electrodes should focus on maximizing GDC surface area. Particularly, GDC electrodes with infiltrated GDC nanoparticles or electro-catalytic nanoparticles may achieve competitive performance compared with the conventional Ni-YSZ electrodes. Although many strategies have been proposed to improve performance of GDC-based electrodes, it is difficult to quantitatively compare all the reported results. Furthermore, the correlation between microstructure and performance of pure GDC electrode are still scarce.Several different types of GDC-based electrodes are fabricated and tested in the unified characterization procedure in this study. Four basic designs are considered, i.e. Ni-GDC, GDC-perovskite composites, GDC electrodes with deposited Ni nanoparticles and pure GDC electrodes. Several strategies to modify the GDC surface area are discussed. In addition, the substantial enhancements in the DPB density and electrochemical performance were achieved by precipitating Ni-nanoparticles directly on sub-micron GDC powders at 2wt.% loading. The performance of electrodes was evaluated by electrochemical impedance spectra measurements with various humidity and temperature conditions. The results showed clear dependance between GDC surface area and electrode performance. At the same time, it should be noted that the electrode active thickness depends on the electrode microstructure. In particular, it is in the range of 5 µm for the pure nano-GDC electrode. When the GDC electrode is thicker than the active thickness, it results in large Ohmic resistance due to the electronic conduction in the porous electrode.[1] A. Nenning, M. Holzmann, J. Fleig, A.K. Opitz, Mater. Adv. 2 (2021) 5422–5431.[2] M. Ouyang, A. Bertei, S.J. Cooper, Y. Wu, P. Boldrin, X. Liu, M. Kishimoto, H. Wang, M. Naylor Marlow, J. Chen, X. Chen, Y. Xia, B. Wu, N.P. Brandon, J. Energy Chemistry. 56 (2021) 98–112.[3] W. Jung, K.L. Gu, Y. Choi, S.M. Haile, Energy Env. Sci. 7 (2014) 1685–1692.

A comprehensive prediction of the electrical properties of graphene, independent of field‐effect transistor (FET) fabrication, could accelerate the development of graphene wafers and electronic materials. Such a capability may also enable the implementation of in‐line inspection techniques during production. In this study, as a preliminary step toward predicting electrical properties solely from images, the relationship between carrier mobility and graphene surface roughness using atomic force microscopy (AFM) is investigated. Although no correlation is observed between carrier mobility and conventional roughness metrics such as arithmetic mean roughness (S a ) and maximum height (S z ), persistent homology analysis—a mathematical framework that captures topological connectivity—revealed distinctly different persistence diagrams for samples with nearly identical S a values but differing carrier mobilities. It is found that graphene structures conforming to pronounced substrate undulations, rather than convex features such as wrinkles or bubbles, led to decreased carrier mobility. This study serves as a foundational investigation, demonstrating the potential to predict the electrical properties of graphene using only surface morphology images, made possible through the application of persistent homology analysis.

Convolutional Neural Network (CNN) is a powerful and successful deep learning technique for a variety of computer vision and image analysis applications. Interpreting and explaining the decisions of CNNs is one of the most challengeable tasks despite its significant success in various image analysis tasks. Topological Data Analysis (TDA) is an approach that exploits algebraic invariants from topology to analyse high dimensional and noisy datasets as well as growing challenges of big data applications. Persistent homology (PH) is an algebraic topology method for measuring topological features of shapes and/or functions at different distance or similarity resolutions. This work is an attempt to investigate the algebraic properties of pretrained CNN convolutional layer filters based on random Gaussian/Uniform distribution. We shall investigate the stability and sensitivity of the condition number of CNN filters during and post the model training with focus on class discriminability of the PH features of the convolved images. We shall demonstrate a strong link between the condition number of the CNN filters and their discriminating power of the PH representation. In particular, we shall establish that if small perturbation added to the original images then feature maps with well-conditioned filters will produce similar topological features to the original image. Our investigation and findings are based on training CNN's with Digits, MNIST and CIFAR-10 datasets. Our ultimate interest in applying the results of these findings in designing appropriate CNN models for classifications of ultrasound tumor scan images. Preliminary results for these applications are encouraging.

In this bachelor thesis three-dimensional scalar data is visualized using isosurfaces. The given data is the output of simulations of T cells in the lymph nodes. Some of these cells produce a biochemical substance of which the concentration distribution is of interest. Peculiarities of the given data are that the values range over several orders of magnitude and that the domain has holes. This leads to holes in the isosurfaces. Difficulties when using isosurfaces are the fact that isosurfaces can be hidden by others and that the resulting image representations can be hard to interpret. These problems are solved by using varying transparencies for different isovalues. The quality of visualizations using isosurfaces also highly depends on the choice and number of the isovalues. In order to choose those isosurfaces that represent important features of the data, topological information is computed. For this purpose, an algorithm originally applied to grayscale images of CT scans is modified to use it on the scalar data. The algorithm computes the Morse complex of the data, which can then be utilized to determine the persistent homology classes and corresponding Betti numbers. All the extracted information is used to gain an improved visualization using isosurfaces.

The persistent homology analysis is applied to the effective Polyakov-line model on a rectangular lattice to investigate the confinement–deconfinement nature. The lattice data are mapped onto the complex Polyakov-line plane without taking the spatial average and then the plane is divided into three domains. This study is based on previous studies for the clusters and the percolation properties in lattice QCD, but the mathematical method of the analyses are different. The spatial distribution of the data in the individual domain is analyzed by using the persistent homology to obtain information of the multiscale structure of center clusters. In the confined phase, the data in the three domains show the same topological tendency characterized by the birth and death times of the holes which are estimated via the filtration of the alpha complexes in the data space, but do not in the deconfined phase. By considering the configuration averaged ratio of the birth and death times of holes, we can construct the nonlocal order parameter of the confinement–deconfinement transition from the multiscale topological properties of center clusters.

Turing patterns can be used to reproduce biological skin patterns. However, the similarity between the reproduced Turing pattern and the actual skin pattern has not been evaluated quantitatively and has only been determined visually. We propose a method for quantitatively evaluating the similarity between the pattern reproduced by the Turing pattern and biological skin patterns using persistent homology, which is a topological data analysis method. Persistent homology can quantitatively extract the structural information of the pattern, allowing an analysis that focuses only on the structure of the biological skin pattern without being affected by variation in the pattern due to individual differences. The experiment tested the effectiveness of persistent homology analysis on multiple Turing patterns generated by varying the parameters of the Gray–Scott model. We used real images of Scomber japonicus as the organisms represented by Turing patterns, and the similarity between the real images and Turing patterns was calculated using persistent homology. The results confirmed the tendency for a high degree of similarity between real images of several S. japonicus and the Turing patterns generated with certain parameters. These results suggest that persistent homology can be used to quantitatively evaluate the reproducibility of Turing patterns.

Since solid oxides electrolysis cells (SOECs) represent a promising technology for efficient CO2 conversion to useful chemical products, there is a demand for durable, highly active, and inexpensive electrode materials for use in these systems. Many metal oxide catalysts suitable for CO2 reduction have been studied, including La0.3Me0.7Fe0.7Cr0.3O3-δ (Me = Ca, Sr; LMFCr), developed by our research group. These catalysts have comparable activity and are much more stable than conventional metal-ionic conductor cermets, known for coke formation and sulfur poisoning. However, while observed catalyst stability can be easily compared for different materials, their activity is harder to differentiate. This is because the overwhelming majority of materials tested are porous in nature, thus making their true active area unknown. To avoid this issue, we are working on determining LMFCr activity and the CO2 reduction mechanism using thin, smooth catalyst layers, obtained by pulsed laser deposition on a YSZ-(001) electrolyte, then using noble metals as the current collector.Preliminary studies of current collector-LMFCr thin film-CO2/CO combinations suggest that the current collector/LMFCr interfaces may have an electrochemical activity that would contribute measurably to that of the LMFCr-gas dual phase boundary interface. Assuming that the metal/LMFCr interface activity would be similar to that at the metal/ionic conductor triple phase boundary, the goal of the present work is to determine the catalytic activity of both Pt and Au, which are the most common current collector materials used in fuel environments, towards the CO2 reduction reaction, with the activity of these metal/YSZ interfaces toward oxygen reduction used as a reference.Two different full cell configurations were used in this work. In one direction, porous Au or Pt layers were produced by metal paste deposition onto both sides of the YSZ electrolyte and then sintered at 600°C. A polymeric YSZ precursor was then infiltrated into the porous metal backbone and sintered at 750°C to form the YSZ phase. To ensure that the counter was as non-polarizable as possible, Pt in air was chosen due to its high activity in oxygen-containing environments, while also depositing it over 5X the area and ensuring 2X the thickness of the catalyst layer at the working electrode. In the porous electrode configuration, the working electrode was exposed to the testing gas, while the counter electrode was exposed in air to achieve as high an activity as possible. In the second configuration, 0.3 mm thick Pt or Au wires were attached to a 250 µm thick YSZ electrolyte to form a point-contact working electrode. A porous LSM-YSZ composite with a geometric surface area of 0.5 cm2 was painted on the opposite side of the electrolyte to serve as the counter electrode, exposing it to the same gas as the working electrode. Electrochemical performance testing for both cell types was conducted in air and CO2 environments at 750°C with a flow rate of 50 SCCM. Morphological and compositional investigation as well as microelectrode triple phase length determination was done using SEM and EDS elemental mapping.Analysis of the EIS and CV data for the porous electrodes showed that the Pt/YSZ and Au/YSZ electrodes are both active towards the oxygen and CO2 reduction reactions. Au is less so, showing up to 40 times lower activity towards oxygen reduction and 3 times lower activity than for CO2 reduction. This would imply that Au is the preferred current collector material for future electrochemical evaluation of metal oxide catalysts. However, SEM studies indicated that Pt and Au cells had different metal particle sizes, so the triple phase boundary length may be not comparable. In addition, the double layer capacitance, often used to estimate the triple phase boundary length, could not be used here due to the high surface inhomogeneity and distribution of time constants across these catalyst layers.To eliminate these issues, microelectrode studies are currently being conducted. Preliminary results show that Au/YSZ is at least 8 times less active in air and 60 times less active in the CO2 environment than Pt/YSZ, with the activity of both of these electrodes controlled by precisely controlled triple phase boundary length determination via SEM. The cyclic voltammetry data also indicate that CO2 reduction does not occur at Au/YSZ through the full potential range (0-1.6 V vs. the counter electrode), which also implies a very low catalytic activity of Au/YSZ. Further studies, including comparison with the porous composite electrode data, are underway. In addition, determination of the reaction steps is being carried out from EIS data equivalent circuit fitting as well as verification through the use of distribution relaxation times technique.

The persistent homology analysis has been widely used to investigate the phase structure and the spatial structure based on the topological properties of the data space via the filtration of the simplicial complex. In this talk, I explained how to apply the persistent homology analysis to the QCD effective model with heavy quarks; i.e., the effective Polyakov-line model and the Potts model with the suitably tuned external magnetic field. In this proceedings, the Potts model results are mainly shown. It is shown that the averaged birth-death time ratio has the same information with the spatial averaged Polyakov-loop and the maximum birth-death time ratio has more information than the averaged birth-death time ratio. Then, the peak structure near the first-order phase transition point and the valley structure before the transition are clarified. In addition, the plateau behavior is found between the first-order transition and the crossover.

The topological analysis of four-dimensional (4D) image-type data is challenged by the immense size that these datasets can reach. This can render the direct application of methods, like persistent homology and convolutional neural networks (CNNs), impractical due to computational constraints. This study aims to estimate the topology type of 4D image-type data cubes that exhibit topological intricateness and size above our current processing capacity. The experiments using synthesised 4D data and a real-world 3D data set demonstrate that it is possible to circumvent computational complexity issues by applying downscaling methods to the data before training a CNN. This is achievable even when persistent homology software indicates that downscaling can significantly alter the homology of the training data. When provided with downscaled test data, the CNN can still estimate the Betti numbers of the original sample cubes with over 80% accuracy, which outperforms the persistent homology approach, whose accuracy deteriorates under the same conditions. The accuracy of the CNNs can be further increased by moving from a mathematically-guided approach to a more vision-based approach where cavity types replace the Betti numbers as training targets.

Topological data analysis in investment decisions

Effect of powder morphology on the microstructural characteristics of La0.6Sr0.4Co0.2Fe0.8O3 cathode: A Kinetic Monte Carlo investigation

Accessible triple-phase boundary length: A performance metric to account for transport pathways in heterogeneous electrochemical materials

This article aimed to explore topological uncertainty in medical imaging, particularly in assessing coronary artery calcification using artificial intelligence (AI). Topological uncertainty refers to ambiguities in spatial and structural characteristics of medical features, which can impact the interpretation of coronary plaques. The article discusses the challenges of integrating AI with topological considerations and the need for specialized methodologies beyond traditional performance metrics. It highlights advancements in quantifying topological uncertainty, including the use of persistent homology and topological data analysis techniques. The importance of standardization in methodologies and ethical considerations in AI deployment are emphasized. It also outlines various types of uncertainty in topological frameworks for coronary plaques, categorizing them as quantifiable and controllable or quantifiable and not controllable. Future directions include developing AI algorithms that incorporate topological insights, establishing standardized protocols, and exploring ethical implications to revolutionize cardiovascular care through personalized treatment plans guided by sophisticated topological analysis. Recognizing and quantifying topological uncertainty in medical imaging as AI emerges is critical. Exploring topological uncertainty in coronary artery disease will revolutionize cardiovascular care, promising enhanced precision and personalization in diagnostics and treatment for millions affected by cardiovascular diseases.