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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Topological graph-based analysis of solid-state ion migration

To accelerate the development of ion conducting materials, we present a general graph-theoretic analysis framework for ion migration in any crystalline structure. The nodes of the graph represent metastable sites of the migrating ion and the edges represent discrete migration events between adjacent sites. Starting from a collection of possible metastable migration sites, the framework assigns a weight to the edges by calculating the individual migration energy barriers between those sites. Connected pathways in the periodic simulation cell corresponding to macroscopic ion migration are identified by searching for the lowest-cost cycle in the periodic migration graph. To exemplify the utility of the framework, we present the automatic analyses of Li migration in different polymorphs of VO(PO 4 ), with the resulting identification of two distinct crystal structures with simple migration pathways demonstrating overall <300 meV migration barriers.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Anomalies in the topology of the temperature fluctuations in the cosmic microwave background: An analysis of the NPIPE and FFP10 data releases

We present a topological analysis of the temperature fluctuation maps from the Planck 2020 Data Release 4 NPIPE dataset and the Planck 2018 Data Release 3 FFP10 dataset. We performed a multiscale analysis in terms of the homology characteristics of the maps, invoking relative homology to account for the analysis in the presence of masks. We performed our analysis for a range of smoothing scales spanning sub- and super-horizon scales corresponding to a full width at half maximum (FWHM) of 5',10',20',40',80',160',320', and 640', and employed simulations based on the standard model for comparison, which assumes the initial fluctuation field to be an isotropic and homogeneous Gaussian random field. Examining the behavior of topological components, represented by the 0D homology group, we find the observations to be approximately 2σ or less deviant from the simulations for all resolutions and scales for the NPIPE dataset. For the FFP10 dataset, we detect a 2.96σ deviation between the observations and simulations at N = 128, FWHM = 80'. For the topological loops, represented by the first homology group, the simulations and observations are consistent within 2σ for most resolutions and scales for both the datasets. However, for the NPIPE dataset, we observe a high deviation between the observation and simulations in the number of loops at FWHM = 320', but at a low dimensionless threshold ν = –2.5. Under a Gaussian assumption, this would amount to a deviation of ~4σ. However, the distribution in this bin is manifestly non-Gaussian and does not obey Poisson statistics either. In the absence of a true theoretical understanding, we simply note that the significance is higher than what may be resolved by 600 simulations, yielding an empirical p-value of at most 0.0016. Specifically in this case, our tests indicate that the numbers arise from a statistically stable regime, despite being based on small numbers. For the FFP10 dataset, the differences are not as strong as for the NPIPE dataset, indicating a 2.77σ deviation at this resolution and threshold. The Euler characteristic, which is the alternating sum of the ranks of relative homology groups, reflects the deviations in the components and loops. To assess the significance of combined levels for a given scale, we employed the empirical and theoretical versions of the χ 2 test as well as the nonparametric Tukey depth test. Although all statistics exhibit a stable distribution, we favor the empirical version of the χ 2 test in the final interpretation, as it indicates the most conservative differences. For the NPIPE dataset, we find that the components and loops differ at more than 95%, but agree within the 99% confidence level with respect to the base model at N = 32, FWHM = 320'. The Euler characteristic at this resolution displays a per mil deviation. In contrast, the FFP10 dataset shows that the observations are consistent with the base model within the 95% confidence level, at this and smaller scales. This is consistent with the observations of the Planck analysis pipeline via Minkowski functionals. For the largest smoothing scale, N = 16, FWHM = 640', both datasets exhibit an anomalous behavior of the loops, where FFP10 data exhibit a deviation that is larger by an order of magnitude than that of the NPIPE dataset. In contrast, the values for the topological components and the Euler characteristic agree between observations and model to within a confidence level of 99%. However, for the largest scales, the statistics are based on low numbers and may have to be regarded with caution. Even though both datasets exhibit mild to significant discrepancies, they also exhibit contrasting behaviors at various instances. Therefore, we do not find it feasible to convincingly accept or reject the null hypothesis. Disregarding the large-scale anomalies that persist at similar scales in WMAP and Planck, observations of the cosmic microwave background are largely consistent with the standard cosmological model within 2σ.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Topological Simplifications of Hypergraphs

Here we study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph into its graph representations, known as the line graph and clique expansion. A topological simplification of such a graph representation induces a simplification of the hypergraph. In simplifying a hypergraph, we allow vertices to be combined if they belong to almost the same set of hyperedges, and hyperedges to be merged if they share almost the same set of vertices. Our proposed approaches are general and mathematically justifiable, and put vertex simplification and hyperedge simplification in a unifying framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Do Neural Networks Trained with Topological Features Learn Different Internal Representations?

There is a growing body of work that leverages features extracted via topological data analysis to train machine learning models. While this field, sometimes known as topological machine learning (TML), has seen some notable successes, an understanding of how the process of learning from topological features differs from the process of learning from raw data is still limited. In this work, we begin to address one component of this larger issue by asking whether a model trained with topological features learns internal representations of data that are fundamentally different than those learned by a model trained with the original raw data. To quantify ``different'', we exploit two popular metrics that can be used to measure the similarity of the hidden representations of data within neural networks, neural stitching and centered kernel alignment. From these we draw a range of conclusions about how training with topological features does and does not change the representations that a model learns. Perhaps unsurprisingly, we find that structurally, the hidden representations of models trained and evaluated on topological features differ substantially compared to those trained and evaluated on the corresponding raw data. On the other hand, our experiments show that in some cases, these representations can be reconciled (at least to the degree required to solve the corresponding task) using a simple affine transformation. We conjecture that this means that neural networks trained on raw data may extract some limited topological features in the process of making predictions.

McGuire, Sarah L.↗
DOE OSTI2021

Materials Fingerprinting Classification

Significant progress in many classes of materials could be made with the availability of experimentally-derived large datasets composed of atomic identities and three-dimensional coordinates. Methods for visualizing the local atomic structure, such as atom probe tomography (APT), which routinely generate datasets comprised of millions of atoms, are an important step in realizing this goal. However, state-of-the-art APT instruments generate noisy and sparse datasets that provide information about elemental type, but obscure atomic structures, thus limiting their subsequent value for materials discovery. The application of a materials fingerprinting process, a machine learning algorithm coupled with topological data analysis, provides an avenue by which here-to-fore unprecedented structural information can be extracted from an APT dataset. As a proof of concept, the material fingerprint is applied to high-entropy alloy APT datasets containing body-centered cubic (BCC) and face-centered cubic (FCC) crystal structures. A local atomic configuration centered on an arbitrary atom is assigned a topological descriptor, with which it can be characterized as a BCC or FCC lattice with near perfect accuracy, despite the inherent noise in the dataset. Finally, this successful identification of a fingerprint is a crucial first step in the development of algorithms which can extract more nuanced information, such as chemical ordering, from existing datasets of complex materials.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Malicious Cyber Activity Detection using Zigzag Persistence

In this study we synthesize zigzag persistence from topological data analysis with autoencoder-based approaches to detect malicious cyber activity, and derive analytic insights. Cybersecurity aims to safeguard computers, networks, and servers from various forms of malicious attacks, including network damage, data theft, and activity monitoring. We focus on the cybersecurity domain and investigate the detection of malicious activity using log data. We consider the dynamics of the log data and explore the changing topology of a hypergraph representation of this data to gain insights into the underlying activity. These hypergraphs capture complex interactions between processes, together with their temporal information. To study the changing topology we use zigzag persistence, which captures how topological features persist at multiple dimensions over time. We observe that this detects malicious activity in a cyber data set. To automate this detection we implement an autoencoder trained on a vectorization of the resulting zigzag persistence barcodes. Our experimental results demonstrate the effectiveness of the autoencoder in detecting malicious activity. Overall, this study highlights the potential of zigzag persistence and its combination with temporal hypergraphs for analyzing cybersecurity log data and detecting malicious behavior.

hypergraphs, temporal hypergraph, topological data↗
DOE OSTI2021

Topological Machine Learning Methods for Power System Responses to Contingencies: Preprint

While deep learning tools, coupled with the emerging machinery of topological data analysis, are proven to deliver various performance gains in a broad range of applications, from image classification to biosurveillance to blockchain fraud detection, their utility in areas of high societal importance such as power system modeling and, particularly, resilience quantification in the energy sector yet remain untapped. To provide fast acting synthetic regulation and contingency reserve services to the grid while having minimal disruptions on customer quality of service, we propose a new topologybased system that depends on neural network architecture for impact metrics classification and prediction in power systems. This novel topology-based system allows one to evaluate the impact of three power system contingency types, namely, in conjunction with transmission lines, transformers, and transmission lines combined with transformers. We show that the proposed new neural network architecture equipped with local topological measures facilitates both more accurate classification of unserved load as well as the amount of unserved load. In addition, we are able to learn complex relationships between electrical properties and local topological measurements on the simulated response to contingencies for NREL-SIIP power system.

graph theory↗
DOE OSTI2023

Seven open problems in applied combinatorics

We present and discuss seven different open problems in applied combinatorics. Additionally, the application areas relevant to this compilation include quantum computing, algorithmic differentiation, topological data analysis, iterative methods, hypergraph cut algorithms, and power systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Distributed Augmentation, Hypersweeps, and Branch Decomposition of Contour Trees for Scientific Exploration

Contour trees describe the topology of level sets in scalar fields and are widely used in topological data analysis and visualization. A main challenge of utilizing contour trees for large-scale scientific data is their computation at scale using highperformance computing. To address this challenge, recent work has introduced distributed hierarchical contour trees for distributed computation and storage of contour trees. However, effective use of these distributed structures in analysis and visualization requires subsequent computation of geometric properties and branch decomposition to support contour extraction and exploration. In this work, we introduce distributed algorithms for augmentation, hypersweeps, and branch decomposition that enable parallel computation of geometric properties, and support the use of distributed contour trees as query structures for scientific exploration. Finally, we evaluate the parallel performance of these algorithms and apply them to identify and extract important contours for scientific visualization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

G-Mapper: Learning a Cover in the Mapper Construction

The Mapper algorithm is a visualization technique in topological data analysis (TDA) that outputs a graph reflecting the structure of a given dataset. However, the Mapper algorithm requires tuning several parameters in order to generate a “nice” Mapper graph. This paper focuses on selecting the cover parameter. We present an algorithm that optimizes the cover of a Mapper graph by splitting a cover repeatedly according to a statistical test for normality. Our algorithm is based on G-means clustering, which searches for the optimal number of clusters in 𝑘-means by iteratively applying the Anderson–Darling test. Our splitting procedure employs a Gaussian mixture model to carefully choose the cover according to the distribution of the given data. In conclusion, experiments for synthetic and real-world datasets demonstrate that our algorithm generates covers so that the Mapper graphs retain the essence of the datasets, while also running significantly faster than a previous iterative method.

G-means clustering↗
DOE OSTI2025

Pulsed Infrared Thermography Nondestructive Imaging of SiC-SiC f Composite Cladding Architectures; Understanding the Performance of SiC-SiC f Composite Cladding Architectures with Cr Coating in Normal Operating and Accident Conditions in LWRs and Advanced Reactors

SiC-SiC f composites, consisting of silicon carbide fibers embedded in a silicon carbide matrix, are advanced materials with high thermal conductivity, temperature stability, and resistance to radiation damage. Traditional methods for quality control of fabricated SiC-SiC f composites involve nondestructive evaluation (NDE) with X-ray computed tomography (XCT). However, XCT imaging of typical SiC-SiC f structures for cladding applications can involve several hours. In this project, we investigate an alternative approach to NDE of SiC-SiC f composites that involves rapid (on the order of seconds) imaging with Pulsed infrared thermography (PIT). PIT images of a planar SiC-SiC f specimen show the structure of the surface monolith layer and internal SiC f structures. The capability of PIT imaging in visualizing SiC f structures is qualitatively confirmed by observing similarity in the PIT and X-ray transmission images of the same specimen. Computer vision analysis of defects in the PIT image of the monolith was performed with thresholding followed by topological structural analysis that computed geometric descriptors, including major/minor axes of fitted ellipses, area, perimeter, Feret diameter, circularity, roundness, and solidity.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Microstructure‐Informed Analysis Framework for Lattice Structures: Guiding Topology‐Material Synergy in Titanium Alloys

In this work we discuss a microstructure‐informed analysis framework for lattice structures that maps the material's microstructural response to guide topology selection and mechanical performance optimization. By coupling geometrical topology with intrinsic material behavior, we demonstrate how anisotropic microstructural response can inform the design of optimized lattice structures. To illustrate this concept, we focus on two distinct classes of titanium alloys: Ti5553 (Ti‐5Al‐5Mo‐5V‐3Cr wt%), which exhibits a predominantly ‐phase microstructure, and Ti64 (Ti‐6Al‐4V wt%), which features a dual‐phase structure. These alloys exhibit markedly different mechanical responses under multiaxial loading in “fully dense” solid form. The strut‐level stress analysis of these alloys reveals how specific microstructural characteristics can guide the selection of appropriate lattice topologies. Two representative lattice configurations, one stretching‐dominated and one bending‐dominated, are evaluated under identical loading conditions to explore how microstructure‐driven design can lead to topology choices that are better suited to accommodate shear or other critical local stress states, thereby enhancing mechanical performance. A strut‐level mechanics‐based analysis is performed to evaluate shear stress distribution and highlight the role of topology‐microstructure synergy and compatibility in determining overall lattice behavior. The findings emphasize the importance of designing structures that are both load‐aware and microstructure‐responsive, enabling more effective material utilization in advanced engineering applications.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Topological Machine Learning Methods for Power System Responses to Contingencies

While deep learning tools, coupled with the emerging machinery of topological data analysis, are proven to deliver various performance gains in a broad range of applications, from image classification to biosurveillance to blockchain fraud detection, their utility in areas of high societal importance such as power system modeling and, particularly, resilience quantification in the energy sector yet remains untapped. To provide fast acting synthetic regulation and contingency reserve services to the grid while having minimal disruptions on customer quality of service, we propose a new topology-based system that depends on a neural network architecture for impact metric classification and prediction in power systems. This novel topology-based system allows one to evaluate the impact of three power system contingency types, in conjunction with transmission lines, transformers, and transmission lines combined with transformers. We show that the proposed new neural network architecture equipped with local topological measures facilitates more accurate classification of unserved load as well as the amount of unserved load. In addition, we are able to learn more about the complex relationships between electrical properties and local topological measurements on their simulated response to contingencies for the NREL-SIIP power system.

contingency analysis↗
DOE OSTI2021

Efficient Topology Design Algorithms for Power Grid Stability

The dynamic response of power grids to small disturbances influences their overall stability. This letter examines the effect of network topology on the linearized time-invariant dynamics of electric power systems. The proposed framework utilizes H 2 -norm based stability metrics to study the optimal placement of lines on existing networks as well as the topology design of new networks. The design task is first posed as an NP-hard mixed-integer nonlinear program (MINLP) that is exactly reformulated as a mixed-integer linear program (MILP) using McCormick linearization. To improve computation time, graph-theoretic properties are exploited to derive valid inequalities (cuts) and tighten bounds on the continuous optimization variables. Moreover, a cutting plane generation procedure is put forth that is able to interject the MILP solver and augment additional constraints to the problem on-the-fly. Finally, the efficacy of our approach in designing optimal grid topologies is demonstrated through numerical tests on the IEEE 39-bus network.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Scalable Computation of Topological Abstractions for Scalar Data

Topological data analysis has become an important tool for large scale scalar data analysis and visualization, efficiently extracting the inherent structure and features of interest of the data. However, with growing dataset sizes and complexity, it is increasingly becoming infeasible to compute topological abstractions of interest in serial and on single machines. This paper presents the state of the art in the scalable computation of topological abstractions on scalar data, in shared memory parallel on single machines, and in distributed memory parallel on multiple machines. We highlight results for set‐based, graph‐based and complex‐based abstractions and organize the state of the art based on this taxonomy. The paper identifies parallelization and distribution techniques common in topological algorithms and highlights further areas of interest with underdeveloped efforts.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Analysis and Comparison of Different Metrics of DC-DC Converters to Determine Fuel Cell Stack Architectures in Heavy Duty Fuel Cell Vehicle Applications

This paper presents a comparative study of the DC-DC converters used in heavy-duty fuel cell electric vehicles for different input fuel cell stack configurations and voltages in terms of various important metrics including efficiency, cost, weight and power density. Contrary to conventional use of an interleaved boost topology, the analysis presented in this paper demonstrates that improved converter metrics can be achieved for an interleaved buck topology that uses a different input fuel cell stack. An insight to the optimal choice of number of interleaved phases for each metric is also presented. Results presented in the tables and plots convey the findings.

Mukherjee, Subho↗
DOE OSTI2025

Dark Energy Survey Year 3 results: $w$CDM cosmology from simulation-based inference with persistent homology on the sphere

We present cosmological constraints from Dark Energy Survey Year 3 (DES Y3) weak lensing data using persistent homology, a topological data analysis technique that tracks how features like clusters and voids evolve across density thresholds. For the first time, we apply spherical persistent homology to galaxy survey data through the algorithm TopoS2, which is optimized for curved-sky analyses and HEALPix compatibility. Employing a simulation-based inference framework with the Gower Street simulation suite, specifically designed to mimic DES Y3 data properties, we extract topological summary statistics from convergence maps across multiple smoothing scales and redshift bins. After neural network compression of these statistics, we estimate the likelihood function and validate our analysis against baryonic feedback effects, finding minimal biases (under $0.3σ$) in the $Ω_\mathrm{m}-S_8$ plane. Assuming the $w$CDM model, our combined Betti numbers and second moments analysis yields $S_8 = 0.821 \pm 0.018$ and $Ω_\mathrm{m} = 0.304\pm0.037$-constraints 70% tighter than those from cosmic shear two-point statistics in the same parameter plane. Our results demonstrate that topological methods provide a powerful and robust framework for extracting cosmological information, with our spherical methodology readily applicable to upcoming Stage IV wide-field galaxy surveys.

Prat, J. [Nordita; Royal Inst. Tech., Sodertalje; ↗
DOE OSTI2023

Comparing Mapper Graphs of Artificial Neuron Activations

The mapper graph is a popular tool from topological data analysis that provides a graphical summary of point cloud data. It has been used to study data from cancer research, sports analytics, neurosciences, and machine learning. In particular, mapper graphs have been used recently to visualize the topology of high-dimensional artificial neural activations from convolutional neural networks and large language models. However, a key question that arises from using mapper graphs across applications is how to compare mapper graphs to study their structural differences. In this paper, we introduce a distance between mapper graphs using tools from optimal transport. We demonstrate the utility of such a distance by studying the topological changes of neural activations across convolutional layers in deep learning, as well as by capturing the loss of structural information for multiscale mapper.

mapper graphs, computational topology, machine lea↗