Engineering topics

Aksoy, Sinan G.

Publications and source records attributed to Aksoy, Sinan G..

At least 19 records

DOE OSTI2024

Unifying Combinatorial and Graphical Methods in Artificial Intelligence

Recently, a new graph Laplacian, called the inner product Laplacian, was introduced which generalizes many existing Laplacians, including the normalized and combinatorial Laplacian and their weighted variants. The key observation behind the inner product Laplacian is that by defining appropriate inner product spaces on the vertices and edges, the standard Laplacians can be recovered as Hodge Laplacians over the simplicial complex formed by the edges and vertices. These inner product spaces form a natural way to incorporate non-combinatorial information into the definition of a domain-specific Laplacian. In particular, in contrast to current domain-specific weighting schemes which rely solely on edge weights, information regarding the similarity of non-adjacent vertices and arbitrary pairs of edges can be effectively incorporated into the Laplacian. In order to illustrate this approach we consider the problem of calculating the potential energy of an atomistic configuration using Graph Neural Networks. In comparison with start-of-the-art approaches, such as SchNet, our approach replaces a learned (via auto-encoder) representation of the atom types with an inner product space on atoms based on scientific knowledge (e.g., electronegativity). We will illustrate how this approach captures key chemical properties of the molecules and compare the energy calculations with state-of-the-art neural network approaches. However, to compute the resulting Laplacian involves a mixture of sparse and dense matrix computation and yields a dense matrix as the basis for the graph convolution. This dense convolutional kernel necessitates moving away from the standard message passing framework for graph neural networks and increases the computational cost of applying the kernel. In order to mitigate these costs we investigate means of leveraging the mixed sparse and dense computations to reduce the overall computational cost and how these approaches can be automatically transferred to energy efficient hardware (e.g., field programmable gate arrays (FPGAs)).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Identifying Sample Provenance From SEM/EDS Automated Particle Analysis via Few-Shot Learning Coupled With Similarity Graph Clustering

Automated particle analysis (APA) provides a vast amount of compositional data via energy-dispersive X-ray spectroscopy along with size and shape data via scanning electron microscopy for individual particles in a sample. In many instances, APA data are leveraged to support identification of the source of a sample based on the detection of particles of a specific composition. Often, the particles that provide context make up a minuscule portion of the sample. Additionally, the interpretation of complex samples can be difficult due to the diversity of compositions both in the mixture and within a particle. In this work, we demonstrate a method to compute and cluster similarity graphs that describe inter-particle relationships within a sample using a multi-modal few-shot learning neural network. Here, as a proof-of-concept, we show that samples known to have been exposed to gunshot residue can be distinguished from samples occasionally mistaken for gunshot residue. Our workflow builds upon standard APA techniques and data processing methods to unveil additional information in a readily interpretable and quantitatively comparable format.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

Scalable Tensor Methods for Nonuniform Hypergraphs

While multilinear algebra appears natural for studying the multiway interactions modeled by hypergraphs, tensor methods for general hypergraphs have been stymied by theoretical and practical barriers. A recently proposed adjacency tensor is applicable to nonuniform hypergraphs, but is prohibitively costly to form and analyze in practice. We develop tensor times same vector (TTSV) algorithms for this tensor which improve complexity from $O(n^r)$ to a low-degree polynomial in $r$, where $n$ is the number of vertices and $r$ is the maximum hyperedge size. Our algorithms are implicit, avoiding formation of the order $r$ adjacency tensor. Here, we demonstrate the flexibility and utility of our approach in practice by developing tensor-based hypergraph centrality and clustering algorithms. We also show these tensor measures offer complementary information to analogous graph-reduction approaches on data, and are also able to detect higher-order structure that many existing matrix-based approaches provably cannot.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Filtering higher-order datasets

Many complex systems often contain interactions between more than two nodes, known as higher-order interactions, which can change the structure of these systems in significant ways. Researchers often assume that all interactions paint a consistent picture of a higher-order dataset's structure. In contrast, the connection patterns of individuals or entities in empirical systems are often stratified by interaction size. Ignoring this fact can aggregate connection patterns that exist only at certain scales of interaction. To isolate these scale-dependent patterns, we present an approach for analyzing higher-order datasets by filtering interactions by their size. We apply this framework to several empirical datasets from three domains to demonstrate that data practitioners can gain valuable information from this approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Fast Parallel Tensor Times Same Vector for Hypergraphs

Hypergraphs are a popular paradigm to rep- resent complex real-world networks exhibiting multi-way relationships of varying sizes. Mining centrality in hyper- graphs via symmetric adjacency tensors has only recently become computationally feasible for large and complex datasets. To enable scalable computation of these and related hypergraph analytics, here we focus on the Sparse Symmetric Tensor Times Same Vector (S3TTVC) oper- ation. We introduce the Compound Compressed Sparse Symmetric (CCSS) format, an extension of the compact CSS format for hypergraphs of varying hyperedge sizes and present a shared-memory parallel algorithm to compute S3TTVC. We experimentally show S3TTVC computation using the CCSS format achieves better performance than the naive baseline, and is subsequently more performant for hypergraph H-eigenvector centrality.

Shivakumar, Shruti↗

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 OSTI2023

Methods and systems for evaluating data transportability in distribution grids

This document describes systems and techniques for evaluating and improving distribution-grid data transportability. These systems and techniques allow engineers to quantify the data transportability of a communication system within or connected to a distribution grid, which represents an ability to transport in real-time telemetry from source locations (e.g., sensors in the distribution grid) to control mechanisms. Distribution engineers can use the sensor readings to perform grid analytics, control operating parameters, and operate protection systems. Distribution engineers can also use the transportability of the communication system to evaluate the observability of the distribution grid, which represents an ability to combine actual measurements and various types of computations (e.g., analytics, estimators, forecasters) from a system model. Distribution engineers can then generate a sensor allocation plan that indicates the number and location of sensors to maximize observability for a fixed sensor cost and/or minimize sensor cost for predetermined observability.

Taft, Jeffrey D.↗

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 OSTI2022

Skew-Symmetric adjacency matrices for clustering directed graphs

Graph clustering methods often critically rely on the symmetry of graph matrices. Developing analogous methods for digraphs often proves more challenging, because digraph matrices are typically asymmetric and not orthogonally diagonalizable. However, researchers have recently proposed several complex-valued Hermitian digraph matrices. In particular, one such representation has been utilized as an input to an algorithm for finding imbalanced cuts. In this work, we establish an algebraic relationship between this matrix and an associated real-valued matrix. We show using this real-valued matrix for imbalanced cut-finding algorithms is not only sufficient but advantageous. Our algorithm uses less memory and asymptotically less computation while provably preserving solution quality. We also show our method can be easily implemented using standing computational building blocks, possesses better numerical properties, and loans itself to a natural interpretation via an objective function relaxation argument. We empirically demonstrate these advantages on real world data sets and show how our algorithm can uncover meaningful cluster structure.

Hayashi, Koby↗

DOE OSTI2022

SpectralFly: Ramanujan Graphs as Flexible and Efficient Interconnection Networks

In recent years, graph theoretic considerations have become increasingly important in the design of HPC interconnection topologies. One approach is to seek optimal or near-optimal families of graphs with respect to a particular graph theoretic property, such as diameter. For example, the SlimFly topology is based on a construction of McKay, Miller, and \v{S}ir\'{a}\v{n} which produces a diameter two graph on a number of nodes approaching the Moore bound, i.e. the largest possible diameter two graph with a fixed radix. Motivated by recent work of Aksoy, Bruillard, Young, and Raugas, we consider topologies which optimize the spectral gap rather than the diameter. In particular, we introduce a novel HPC topology, SpectralFly, designed around the Ramanujan graph construction of Lubotzky, Phillips, and Sarnak (LPS). In this work, we show that the combinatorial properties, such as diameter, bisection bandwidth, average path length, and resilience to link failure, of SpectralFly topologies are better than, or comparable to, similarly constrained DragonFly, SlimFly, and BundleFly topologies. Additionally, we simulate the performance of SpectralFly topologies on a representative sample of physics-inspired HPC workloads using the Structure Simulation Toolkit Macroscale Element Library simulator and demonstrate considerable benefit to using LPS construction as the basis of the SpectralFly topology.

graphs and networks, network topology, interconnec↗

DOE OSTI2022

Models and Methods for Sparse (Hyper)Network Science in Business, Industry, and Government

The authors are hosting an AMS sponsored Mathematics Research Community (MRC) focusing on two themes that have garnered intense attention in network models of complex relational data: (1) how to faithfully model multi-way relations in hypergraphs, rather than only pairwise interactions in graphs; and (2) challenges posed by modelling networks with extreme sparsity. Here we introduce and explore these two themes and their challenges. In this work, we hope to generate interest from researchers in pure and applied mathematics and computer science.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Structural Controllability Assessment for Inverter-Based Microgrids

Enhanced inverter-based controls are considered for microgrids, which use additional actuation beyond a droop-like term. Shaping of the microgrid’s small-signal dynamics using such enhanced controls is posed as a structural controllability problem. A graph-theoretic characterization of structural controllability is obtained, in terms of the concept of zero-forcing sets.Two benchmark test systems are used to illustrate the selection of locations where enhanced controls should be applied, based on the graph-theoretic analysis. These examples indicate that small-signal characteristics can be shaped using a relatively small number of enhanced controls

microgrids, zero-forcing, structural controlabilit↗

DOE OSTI2021

Parallel Algorithms for Efficient Computation of High-Order Line Graphs of Hypergraphs

This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are set-valued. To date, in most situations, entities in a hypergraph are considered connected as long as there is at least one common ``neighbor''. However, minimal commonality sometimes discards the ``strength'' of connections and interactions among groups. To this end, considering the ``width'' of a connection, referred to as the \emph{$s$-overlap} of neighbors, provides more meaningful insights into how closely the communities or entities interact with each other. In addition, $s$-overlap computation is the fundamental kernel to construct the line graph of a hypergraph, a low-order approximation of the hypergraph which can carry significant information about the original hypergraph. Subsequent stages of a data analytics pipeline then can apply highly-tuned graph algorithms on the line graph to reveal important features. Given a hypergraph, computing the $s$-overlaps by exhaustively considering all pairwise entities can be computationally prohibitive. To tackle this challenge, we develop efficient algorithms to compute $s$-overlaps and the corresponding line graph of a hypergraph. We propose several heuristics to avoid execution of redundant work and improve performance of the $s$-overlap computation. Our parallel algorithm, combined with these heuristics, is orders of magnitude (more than $10\times$) faster than the naive algorithm in all cases and the SpGEMM algorithm with filtration in most cases (especially with large $s$ value).

hypergraph algorithms, graph algorithms, parallel ↗

DOE OSTI2021

Explaining and predicting human behavior and social dynamics in simulated virtual worlds: reproducibility, generalizability, and robustness of causal discovery methods

Ground Truth program was designed to evaluate social science modeling approaches using simulation test beds with ground truth intentionally and systematically embedded to understand and model complex Human Domain systems and their dynamics Lazer et al. (Science 369:1060–1062, 2020). Our multidisciplinary team of data scientists, statisticians, experts in Artificial Intelligence (AI) and visual analytics had a unique role on the program to investigate accuracy, reproducibility, generalizability, and robustness of the state-of-the-art (SOTA) causal structure learning approaches applied to fully observed and sampled simulated data across virtual worlds. In addition, we analyzed the feasibility of using machine learning models to predict future social behavior with and without causal knowledge explicitly embedded. In this paper, we first present our causal modeling approach to discover the causal structure of four virtual worlds produced by the simulation teams—Urban Life, Financial Governance, Disaster and Geopolitical Conflict. Our approach adapts the state-of-the-art causal discovery (including ensemble models), machine learning, data analytics, and visualization techniques to allow a human-machine team to reverse-engineer the true causal relations from sampled and fully observed data. We next present our reproducibility analysis of two research methods team’s performance using a range of causal discovery models applied to both sampled and fully observed data, and analyze their effectiveness and limitations. We further investigate the generalizability and robustness to sampling of the SOTA causal discovery approaches on additional simulated datasets with known ground truth. Our results reveal the limitations of existing causal modeling approaches when applied to large-scale, noisy, high-dimensional data with unobserved variables and unknown relationships between them. We show that the SOTA causal models explored in our experiments are not designed to take advantage from vasts amounts of data and have difficulty recovering ground truth when latent confounders are present; they do not generalize well across simulation scenarios and are not robust to sampling; they are vulnerable to data and modeling assumptions, and therefore, the results are hard to reproduce. Finally, when we outline lessons learned and provide recommendations to improve models for causal discovery and prediction of human social behavior from observational data, we highlight the importance of learning data to knowledge representations or transformations to improve causal discovery and describe the benefit of causal feature selection for predictive and prescriptive modeling.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Directional Laplacian Centrality for Cyber Situational Awareness

Cyber operations is drowning in diverse, high-volume, multi-source data. To get a full picture of current operations and identify malicious events and actors, analysts must see through data generated by a mix of human activity and benign automated processes. Although many monitoring and alert systems exist, they typically use signature-based detection methods. We introduce a general method rooted in spectral graph theory to discover patterns and anomalies without a priori knowledge of signatures. We derive and propose a new graph-theoretic centrality measure based on the derivative of the graph Laplacian matrix in the direction of a vertex. To build intuition about our measure, we show how it identifies the most central vertices in standard network datasets and compare to other graph centrality measures. Finally, we focus our attention on studying its effectiveness in identifying important IP addresses in network flow data. Using both real and synthetic network flow data, we conduct several experiments to test our measure’s sensitivity to two types of injected attack profiles and show that vertices participating in injected attack profiles exhibit noticeable changes in our centrality measures, even when the injected anomalies are relatively small, and in the presence of simulated network dynamics.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2021

Hypernetwork Science: From Multidimensional Networks to Computational Topology

As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra, lattice theory, and topology. They are able to represent complex systems interactions more faithfully than graphs and networks, while also being some of the simplest classes of systems representing topological structures as collections of multidimensional objects connected in a particular pattern. In this paper we discuss the role of (undirected) hypergraphs in the science of complex networks, and provide a mathematical overview of the core concepts needed for hypernetwork modeling, including duality and the relationship to bicolored graphs, quantitative adjacency and incidence, the nature of walks in hypergraphs, and available topological relationships and properties. We close with a brief discussion of two example applications: biomedical databases for disease analysis, and domain-name system (DNS) analysis of cyber data.

Joslyn, Cliff A.↗

DOE OSTI2021

Spectral Threshold for Extremal Cyclic Edge-Connectivity

In this report, the cyclic edge-connectivity of a graph G is the least k such that there exists a set of k edges whose removal disconnects G into components where every component contains a cycle. We show that for graphs of minimum degree at least 3 and girth g at least 4, the cyclic edge-connectivity is bounded above by (Δ-2)g where Δ is the maximum degree. We then prove that if the second eigenvalue of the adjacency matrix of a d-regular graph of girth g ≥ 4 is sufficiently small, then the cyclic edge-connectivity is (d-2)g, providing a spectral condition for when this upper bound on cyclic edge-connectivity is tight.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Hypergraph Random Walks, Laplacians, and Clustering

We propose a flexible framework for clustering hypergraph-structured data based on recently proposed random walks utilizing edge-dependent vertex weights. When incorporating edge-dependent vertex weights (EDVW), a weight is associated with each vertex-hyperedge pair, yielding a weighted incidence matrix of the hypergraph. Such weightings have been utilized in term-document representations of text data sets. We explain how random walks with EDVW serve to construct different hypergraph Laplacian matrices, and then develop a suite of clustering methods that use these incidence matrices and Laplacians for hypergraph clustering. Using 20Newsgroup, U.S. patent, Reuters' Corpus Volume 1, and genetics data sets, we compare the performance of these clustering algorithms experimentally against a variety of existing hypergraph clustering methods. We show that the proposed methods produce higher-quality clusters.

hypergraphs, clustering, laplacian, random walk, M↗