SEARCH · Engineering Papers
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Topological Data Analysis for Adversarial Detection (LANL O4937) - Detects adversarial examples in vision-language models using persistent homology and two-sample testing. Combines TDA features from CLIP embeddings with statistical methods (ME, SCF, SAMMD, C2ST) for robust detection across ImageNet, CIFAR-10/100.
This software package is for distributed computation of persistent (co)homology. It is primarily intended for Topological Data Analysis (TDA) audience and scientists who use TDA methods and apply them to datasets that are too big to handle on a single machine. There are very few codes available for this; Cadmus outperforms DIPHA, if the user is interested in cohomology. The accompanying paper explaining the algorithm was accepted to ALENEX 26.
This final technical report describes the activities undertaken through Department of Energy, Office of Science, Advanced Scientific Computing Research Early Career award DE-SC-0019039, “Analyzing Multifaceted Scientific Data with Topological Analytics." This report summarizes contributions made toward the research of visualization, machine learning, and topological data analysis of complex simulation data.
A short presentation highlighting using machine learning and topological data analysis to address the challenges of assuring and securing machine learning enabled systems.
Advanced manufacturing research and development is typically small-scale, owing to costly experiments associated with these novel processes. Deep learning techniques could help accelerate this development cycle but frequently struggle in small-data regimes like the advanced manufacturing space. While prior work has applied deep learning to modeling visually plausible advanced manufacturing microstructures, little work has been done on data-driven modeling of how microstructures are affected by heat treatment, or assessing the degree to which synthetic microstructures are able to support existing workflows. We propose to address this gap by using invertible neural networks (normalizing flows) to model the effects of heat treatment, e.g., tempering. The model is developed using scanning electron microscope imagery from samples produced using shear-assisted processing and extrusion (ShAPE) manufacturing. This approach not only produces visually and topologically plausible samples, but also captures information related to a sample’s material properties or experimental process parameters. We also demonstrate that topological data analysis, used in prior work to characterize microstructures, can also be used to stabilize model training, preserve structure, and improve downstream results. We assess directions for future work and identify our approach as an important step towards end-to-end deep learning system for accelerating advanced manufacturing research and development.
The increasing interest in big data applications is ushering in a large effort in seeking new, efficient, and adapted data models to reduce complexity, while preserving maximal intrinsic information. Graph-based models have recently been getting a lot of attention on account of their intuitive and direct connection to the data. The cost of these models, however, is to some extent giving up geometric insight as well as algebraic flexibility. Topology, as an intermediate analysis medium, focuses on coarse structures of an object/signal in general. It affords a formalism of transitioning from a local to a global description of an object, while providing significant information, which respects the local structure of measurements. It may also support a global visualization (e.g., data variation trends) and enhances the understanding of the underlying phenomenon. Throughout this article, measurements may be considered proximal in various ways, depending on the specific application, and the selected proximity metrics are subsequently used in the construction of a graph structure, thus highlighting various groups of neighboring data. As described later, these groups, often based on proximity criteria, are represented by n-simplices, where n + 1 corresponds to the number of points in an associated group. Collectively, they form what is (and will be throughout) referred to as a simplicial complex, a special representation of a topological space. We find the key advantage of computational topology is its inherently algebraic structure on the basic elements of the resulting graph-like structure.
This paper presents a practical approach for the optimization of topological simplification, a central pre-processing step for the analysis and visualization of scalar data. Given an input scalar field f and a set of “signal” persistence pairs to maintain, our approaches produces an output field g that is close to f and which optimizes (i) the cancellation of “non-signal” pairs, while (ii) preserving the “signal” pairs. In contrast to pre-existing simplification algorithms, our approach is not restricted to persistence pairs involving extrema and can thus address a larger class of topological features, in particular saddle pairs in three-dimensional scalar data. Our approach leverages recent generic persistence optimization frameworks and extends them with tailored accelerations specific to the problem of topological simplification. Extensive experiments report substantial accelerations over these frameworks, thereby making topological simplification optimization practical for real-life datasets. Our approach enables a direct visualization and analysis of the topologically simplified data, e.g., via isosurfaces of simplified topology (fewer components and handles). We apply our approach to the extraction of prominent filament structures in three-dimensional data. Specifically, we show that our pre-simplification of the data leads to practical improvements over standard topological techniques for removing filament loops. Here, we also show how our approach can be used to repair genus defects in surface processing. Finally, we provide a C++ implementation for reproducibility purposes.
High-order finite element methods (HO-FEM) are gaining popularity in the simulation community due to their success in solving complex flow dynamics. There is an increasing need to analyze the data produced as output by these simulations. Simultaneously, topological analysis tools are emerging as powerful methods for investigating simulation data. Yet, most of the current approaches to topological analysis have had limited application to HO-FEM simulation data for two reasons. First, the current topological tools are designed for linear data (polynomial degree one), but the polynomial degree of the data output by these simulations is typically higher (routinely up to polynomial degree six). Second, the simulation data and derived quantities of the simulation data have discontinuities at element boundaries, and these discontinuities do not match the input requirements for the topological tools. One solution to both issues is to transform the high-order data to achieve low-order, continuous inputs for topological analysis. Nevertheless, there has been little work evaluating the possible transformation choices and their downstream effect on the topological analysis. We perform an empirical study to evaluate two commonly used data transformation methodologies along with the recently introduced L-SIAC filter for processing high-order simulation data. Our findings indicate diverse behaviors are possible. We offer some guidance about how best to consider a pipeline of topological analysis of HO-FEM simulations with the currently available implementations of topological analysis.
Explore the source record for details and available documents.
Neural manifolds summarize the intrinsic structure of the information encoded by a population of neurons. Advances in experimental techniques have made simultaneous recordings from multiple brain regions increasingly commonplace, raising the possibility of studying how these manifolds relate across populations. However, when the manifolds are nonlinear and possibly code for multiple unknown variables, it is challenging to extract robust and falsifiable information about their relationships. We introduce a framework, called the method of analogous cycles, for matching topological features of neural manifolds using only observed dissimilarity matrices within and between neural populations. We demonstrate via analysis of simulations and in vivo experimental data that this method can be used to correctly identify multiple shared circular coordinate systems across both stimuli and inferred neural manifolds. Conversely, the method rejects matching features that are not intrinsic to one of the systems. Further, as this method is deterministic and does not rely on dimensionality reduction or optimization methods, it is amenable to direct mathematical investigation and interpretation in terms of the underlying neural activity. We thus propose the method of analogous cycles as a suitable foundation for a theory of cross-population analysis via neural manifolds.
The RAVEN code has been under development at the Idaho National Laboratory since 2012. Its main goal is to create a multi-purpose platform for the deploying of all the capabilities needed for Probabilistic Risk Assessment, uncertainty quantification, data mining analysis and optimization studies. RAVEN has currently reached a good level of maturity in terms of deployed state-of-art and advanced capabilities. The main subject of this report is to show the activities that have been recently accomplished: • Implementation of ensemble modeling for time-series, and • initial implementation of model validation for surrogate models, and • advanced visualization capability for topology based data analysis The development of ensemble modeling for time-series has been performed in order to begin tackling the needs of those RISMC applications that need to communicate 1-Dimensional information (e.g. power histories, etc.) among different models. In this document the implementation details and an application example is reported. The second subject of this report is about the initial development of methods, within the RAVEN framework, to assess the validity of the predictive capabilities of surrogate models. Indeed, after the construction of a surrogate tight to a certain physical model, it is crucial to assess the goodness of its representation, in order to be confident with its prediction. In this initial activity, a cross-validation technique has been employed. This report will highlight the implementation details and proof its correct implementation by an application example. The final subject of this report is about the implementation of advanced visualization capability in RAVEN, for interactive data analysis. Indeed, RAVEN offers several post-processing capabilities that can structurally decompose data extracted from experimental results offering both data clustering/partitioning and dimensionality reduction techniques. A disadvantage of the workflow available in RAVEN is that it treats these as black box operations and the user is expected to know specific information about their data including the number of partitions to expect in some cases or the “correct” parameter settings for a particular algorithm. In order to overcome this limitation, it has been added an interactive user interface that can be run in RAVEN to explore different parameter settings on the fly specifically for the topological post-processor and allows the user to explore the data interactively. The design of this user interface is generalizable to other algorithms and can be used as a model to generate more dynamic and user-friendly visualization capabilities within RAVEN.
In many scientific endeavors, increasingly abstract representations of data allow for new interpretive methodologies and conceptualization of phenomena. For example, moving from raw imaged pixels to segmented and reconstructed objects allows researchers new insights and means to direct their studies toward relevant areas. Thus, the development of new and improved methods for segmentation remains an active area of research. With advances in machine learning and neural networks, scientists have been focused on employing deep neural networks such as U-Net to obtain pixel-level segmentations, namely, defining associations between pixels and corresponding/referent objects and gathering those objects afterward. Topological analysis, such as the use of the Morse-Smale complex to encode regions of uniform gradient flow behavior, offers an alternative approach: first, create geometric priors, and then apply machine learning to classify. This approach is empirically motivated since phenomena of interest often appear as subsets of topological priors in many applications. Using topological elements not only reduces the learning space but also introduces the ability to use learnable geometries and connectivity to aid the classification of the segmentation target. Here, in this article, we describe an approach to creating learnable topological elements, explore the application of ML techniques to classification tasks in a number of areas, and demonstrate this approach as a viable alternative to pixel-level classification, with similar accuracy, improved execution time, and requiring marginal training data.
Extreme wind phenomena play a crucial role in the efficient operation of wind farms for renewable energy generation. However, existing detection methods are computationally expensive, limited to specific coordinate. In real-world scenarios, understanding the occurrence of these phenomena over a large area is essential. Therefore, there is a significant demand for a fast and accurate approach to forecast such events. In this paper, we propose a novel method for detecting wind phenomena using topological analysis, leveraging the gradient of wind speed or critical points in a topological framework. By extracting topological features from the wind speed profile within a defined region, we employ topological distance to identify extreme wind phenomena. Our results demonstrate the effectiveness of utilizing topological features derived from regional wind speed profiles. We validate our approach using high-resolution simulations with the Weather Research and Forecasting model (WRF) over a month in the US East Coast.
Extreme wind phenomena play a crucial role in the efficient operation of wind farms for renewable energy generation. However, existing detection methods are computationally expensive, limited to specific coordinate. In real-world scenarios, understanding the occurrence of these phenomena over a large area is essential. Therefore, there is a significant demand for a fast and accurate approach to forecast such events. In this paper, we propose a novel method for detecting wind phenomena using topological analysis, leveraging the gradient of wind speed or critical points in a topological framework. By extracting topological features from the wind speed profile within a defined region, we employ topological distance to identify extreme wind phenomena. Our results demonstrate the effectiveness of utilizing topological features derived from regional wind speed profiles. We validate our approach using high-resolution simulations with the Weather Research and Forecasting model (WRF) over a month in the US East Coast.
Abstract We propose a novel method for the computation of Jacobi sets in 2D domains. The Jacobi set is a topological descriptor based on Morse theory that captures gradient alignments among multiple scalar fields, which is useful for multi-field visualization. Previous Jacobi set computations use piecewise linear approximations on triangulations that result in discretization artifacts like zig-zag patterns. In this paper, we utilize a local bilinear method to obtain a more precise approximation of Jacobi sets by preserving the topology and improving the geometry. Consequently, zig-zag patterns on edges are avoided, resulting in a smoother Jacobi set representation. Our experiments show a better convergence with increasing resolution compared to the piecewise linear method. We utilize this advantage with an efficient local subdivision scheme. Finally, our approach is evaluated qualitatively and quantitatively in comparison with previous methods for different mesh resolutions and across a number of synthetic and real-world examples.
Zigzag filtrations of simplicial complexes generalize the usual filtrations by allowing simplex deletions in addition to simplex insertions. The barcodes computed from zigzag filtrations encode the evolution of homological features. Although one can locate a particular feature at any index in the filtration using existing algorithms, the resulting representatives may not be compatible with the zigzag: a representative cycle at one index may not map into a representative cycle at its neighbor. For this, one needs to compute compatible representative cycles along each bar in the barcode. It is known that the barcode for a zigzag filtration with m insertions and deletions can be computed $O(m^ω)$ in time, where $ω < 2.373$ is the matrix multiplication exponent. However, it is not known how to compute the compatible representatives so efficiently. For a non-zigzag filtration, the classical matrix-based algorithm provides representatives in $O(m^3)$ time, which can be improved to $O(m^ω)$. However, no known algorithm for zigzag filtrations computes the representatives with the $O(m^3)$ time bound. We present an $O(m^3 n)$ time algorithm for this problem, where $n ≤ m$ is the size of the largest complex in the filtration.
Topological abstractions offer a method to summarize the behavior of vector fields, but computing them robustly can be challenging due to numerical precision issues. One alternative is to represent the vector field using a discrete approach, which constructs a collection of pairs of simplices in the input mesh that satisfies criteria introduced by Forman's discrete Morse theory. While numerous approaches exist to compute pairs in the restricted case of the gradient of a scalar field, state-of-the-art algorithms for the general case of vector fields require expensive optimization procedures. This paper introduces a fast, novel approach for pairing simplices of two-dimensional, triangulated vector fields that do not vary in time. The key insight of our approach is that we can employ a local evaluation, inspired by the approach used to construct a discrete gradient field, where every simplex in a mesh is considered by no more than one of its vertices. Specifically, we observe that for any edge in the input mesh, we can uniquely assign an outward direction of flow. We can further expand this consistent notion of outward flow at each vertex, which corresponds to the concept of a downhill flow in the case of scalar fields. Working with outward flow enables a linear-time algorithm that processes the (outward) neighborhoods of each vertex one-by-one, similar to the approach used for scalar fields. Here, we couple our approach to constructing discrete vector fields with a method to extract, simplify, and visualize topological features. Empirical results on analytic and simulation data demonstrate drastic improvements in running time, produce features similar to the current state-of-the-art, and show the application of simplification to large, complex flows.
Persistent cohomology is a powerful technique for discovering topological structure in data. Strategies for its use in neuroscience are still undergoing development. We comprehensively and rigorously assess its performance in simulated neural recordings of the brain's spatial representation system. Grid, head direction, and conjunctive cell populations each span low-dimensional topological structures embedded in high-dimensional neural activity space. We evaluate the ability for persistent cohomology to discover these structures for different dataset dimensions, variations in spatial tuning, and forms of noise. We quantify its ability to decode simulated animal trajectories contained within these topological structures. We also identify regimes under which mixtures of populations form product topologies that can be detected. Our results reveal how dataset parameters affect the success of topological discovery and suggest principles for applying persistent cohomology, as well as persistent homology, to experimental neural recordings.