Mapping state transition susceptibility in quantum annealing
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75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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Results for “Graph algorithms”
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Graph Sparsification by Approximate matrix Multiplication
Graphs arising in statistical problems, signal processing, large networks, combinatorial optimization, and data analysis are often dense, which causes both computational and storage bottlenecks. One way of sparsifying a weighted graph, while sharing the same vertices as the original graph but reducing the number of edges, is through spectral sparsification. We study this problem through the perspective of RandNLA. Specifically, we utilize randomized matrix multiplication to give a clean and simple analysis of how sampling according to edge weights gives a spectral approximation to graph Laplacians, without requiring spectral information. Through the CR–MM algorithm, we attain a simple and computationally efficient sparsifier whose resulting Laplacian estimate is unbiased and of minimum variance. Here, we define a new notion of additive spectral sparsifiers, which has not been considered in the literature.
97 MATHEMATICS AND COMPUTING↗
nuclear-score-maximization v1.0
This software library presents efficient and multithreaded implementations of matrix low rank approximation via column selection in C++17 code. The algorithms are described in Fornace, Mark, and Michael Lindsey. "Column and row subset selection using nuclear scores: algorithms and theory for Nystro m approximation, CUR decomposition, and graph Laplacian reduction." arXiv preprint arXiv:2407.01698 (2024). The presented methods are by-and-large ver novel, have provable approximation guarantees, multiple use-cases, and exhibit higher quality approximations on a variety of studied examples.
Fornace, Mark↗
Resilience Assessment Framework For Electric Distribution Systems Performance Under Extreme Conditions
The devastating impact of extreme weather-related events is increasingly evident on power grids, especially on distribution grids. The severity of their potential impact calls for 1) developing a suitable resilience assessment framework to capture the system performance and 2) assessing relevant mitigative strategies to lessen the impact of such events. This paper proposes a framework to identify grid vulnerabilities using the energy-at-risk concept to select, disconnect and isolate grid portions due to a resilience event. The proposed framework mainly consists of two steps; i) processing the utility's available infrastructure, i.e., a network model, possible switching combinations, and outage information for those combinations, as a graph-based database, and ii) implementing a novel optimal switching algorithm leveraging database and grid simulated metrics. These switching actions are generated to implement load curtailment in a rolling manner during anticipated grid scarcity conditions. In this study, a test case is created using two taxonomy feeders and is simulated against an extreme temperature event, e.g., a long, relatively cold, and prolonged freeze peak, thereby creating stress on the grid. It is demonstrated that the proposed framework allows utilities to predict the energy-at-risk during such resilience events and design suitable outage management strategies.
Poudel, Shiva↗
Classification of dynamical Lie algebras generated by spin interactions on undirected graphs
Dynamical Lie algebras (DLAs) are a versatile tool for various topics that span from the expressibility-trainability of variational quantum algorithms (VQAs), to simulation of many body Hamiltonians. Quantum gates and most of the Hamiltonians of interest consist of local interactions; therefore, the analysis of all possible DLAs generated by 1- and 2-local operators is crucial for quantum simulation and VQAs on current hardware. Previously in [R. Wiersema et al ., npj Quantum Inf. 10 , 110 (2024)], we analyzed the DLAs on linear, circular and all-to-all topologies, and obtained results about their dimensions and algebraic structure. Here, in this work, we extend our analysis into any possible hardware topology and provide a classification of all DLAs generated by Pauli strings on any undirected interaction graph. Our results indicate that the DLAs depend solely on whether the connectivity or interaction graph is bipartite or not. In addition, we find that the non-trivial polynomially scaling DLAs appear only on 1D line or circle topologies, and all other DLAs have dimensions scaling exponentially with the system size. Together with the current VQA literature, our results imply that either the majority of VQAs are non-trainable, or we are yet to understand the role of DLAs on the trainability of VQAs.
Algebraic structures↗
Graph Identification of Proteins in Tomograms (GRIP-Tomo) 2.0: Topologically aware classification for proteins
Cryo-electron tomography (cryo-ET) enables structural characterization of biomolecules under near-native conditions. Existing approaches for interpreting the resulting three-dimensional volumes are computationally expensive and have difficulty interpreting density associated with small proteins/complexes. To explore alternate approaches for identifying proteins in cryo-ET data we pursued a Graph Network and topologically invariant approach. Here, we report on a fast algorithm that classifies particles by searching for nuances of evolutionarily conversed motifs and the geometrical characteristics of protein structure. GRIP-Tomo 2.0 is a machine-learning pipeline that extracts interpretable topological features of protein structures within noisy experimental backgrounds. Compared to version 1.0, the new pipeline includes three upgrades that significantly improve performance including synthetic tomogram generation simulating realistic noise, graph-based persistent feature extraction as protein fingerprints, and high-performance computing acceleration. GRIP-Tomo 2.0 achieves over 90% accuracy in classifying between proteins and noise using both real and synthetic datasets which represents a foundational step toward advancing cryo-ET workflows and empowering automated visual proteomics.
Li, Chengxuan↗
Acceleration of Graph Neural Network-Based Prediction Models in Chemistry via Co-Design Optimization on Intelligence Processing Units
Atomic structure prediction and associated property calculations are the bedrock of chemical physics. Since high-fidelity ab initio modeling techniques for computing the structure and properties can be prohibitively expensive, this motivates the development of machine-learning (ML) models that make these predictions more efficiently. Training graph neural networks over large atomistic databases introduces unique computational challenges such as the need to process millions of small graphs with variable size and support communication patterns that are distinct from learning over large graphs such as social networks. We demonstrate a novel hardware-software co-design approach to scale up the training of atomistic graph neural networks (GNN) for structure and property prediction. First, to eliminate redundant computation and memory associated with alternative padding techniques and to improve throughput via minimizing communication, we formulate the effective coalescing of the batches of variable-size atomistic graphs as the bin packing problem and introduce a hardware-agnostic algorithm to pack these batches. In addition, we propose hardware-specific optimizations including a planner and vectorization for the gather-scatter operations targeted for Graphcore’s Intelligence Processing Unit (IPU), as well as model-specific optimizations such as merged communication collectives and optimized softplus. Putting these all together, we demonstrate the effectiveness of the proposed co-design approach by providing an implementation of a well-established atomistic GNN on the Graphcore IPUs. We evaluate the training performance on multiple atomistic graph databases with varying degrees of graph counts, sizes and sparsity. Here, we demonstrate that such a co-design approach can reduce the training time of atomistic GNNs and can improve the performance by up to 1.5× compared to the baseline implementation of the model on the IPUs. Additionally, we compare our IPU implementation with a Nvidia GPU-based implementation and show that our atomistic GNN implementation on the IPUs can run 1.8× faster on average compared to the execution time on the GPUs.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
SNNVis: Visualizing Graph Embedding of Evolutionary Optimization for Spiking Neural Networks
While Spiking Neural Networks (SNNs) show a lot of promise, it is difficult to optimize them because applying traditional gradient-based optimization techniques is difficult. Even though evolutionary algorithms (EAs) have been shown to promise to optimize SNNs, understanding the relationship between evolving the characteristics of SNNs and their performance to improve the optimization algorithm is challenging because of the complex characteristics and huge population size. We propose visual analytics with novel graph embedding for evolutionary SNNs to address the challenges. While existing graph embedding techniques have limitations in preserving the specific features of the nodes and edges, our approach maintains them. Also, we develop visual analytics for understanding the relationship between the network performance and the features of nodes and edges and exploring and analyzing the evolving SNNs to build insights into improving the EA.
Chae, Junghoon [ORNL] (ORCID:0000000206016746)↗
buhito
buhito is a Python library for graph analysis and machine learning. Graphs can represent networks with objects as nodes and their relationships as edges. buhito focuses on graphlet methods that study graphs through enumerating their component subgraphs to enable interpretable and fast models of complex systems. The package provides tools for different algorithmic designs for computing, analyzing, and applying graphlets to research problems such as machine learning, data compression, and anomaly detection in graph-structured data. A central feature is performing decomposition data analysis on graphs for machine learning models. Implemented in Python and built upon open-source scientific libraries such as NetworkX, NumPy, and SciPy, buhito provides high-performance methods for researchers exploring the mathematical and computational foundations of graphlet analysis applicable to systems of different sizes.
Pimonova, Yulia↗
OpenSn: A massively parallel, open-source simulation environment for discrete ordinates radiation transport
OpenSn is an open-source, massively parallel deterministic radiation transport code for solving the discrete-ordinates ( S N ) form of the Boltzmann transport equation on unstructured, arbitrary polyhedral meshes. It supports high-fidelity simulations involving steady-state, eigenvalue, and adjoint problems for neutral particles (e.g., neutrons, photons, multi-particles), using the multigroup approximation in energy. OpenSn combines angular discretization via discrete ordinates with a discontinuous Galerkin finite element method (DGFEM) in space, enabling accurate resolution of transport physics on arbitrary polyhedral cells, included locally refined spatial grids. It includes multiple angular quadrature types, including locally refined angular quadratures. Written in modern C++ with a Python API, OpenSn runs efficiently on platforms ranging from laptops to supercomputers. The transport sweep algorithm is implemented using a task-based, directed-acyclic-graph (DAG) approach for each angle and supports asynchronous parallelism across thousands of MPI ranks. Group-set aggregation improves compute intensity, and synthetic acceleration techniques (e.g., diffusion synthetic acceleration, second-moment method) enhance solver convergence. OpenSn has been verified on reactor physics problems and demonstrated excellent weak and strong scaling performance on more than 32,768 processes, making it a versatile and robust platform for large-scale transport simulations in complex geometries.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Graph theory approach to determine configurations of multidentate and high coverage adsorbates for heterogeneous catalysis
Abstract Heterogeneous catalysts constitute a crucial component of many industrial processes, and to gain an understanding of the atomic-scale features of such catalysts, ab initio density functional theory is widely employed. Recently, growing computational power has permitted the extension of such studies to complex reaction networks involving either high adsorbate coverages or multidentate adsorbates, which bind to the surface through multiple atoms. Describing all possible adsorbate configurations for such systems, however, is often not possible based on chemical intuition alone. To systematically treat such complexities, we present a generalized Python-based graph theory approach to convert atomic scale models into undirected graph representations. These representations, when combined with workflows such as evolutionary algorithms, can systematically generate high coverage adsorbate models and classify unique minimum energy multidentate adsorbate configurations for surfaces of low symmetry, including multi-elemental alloy surfaces, steps, and kinks. Two case studies are presented which demonstrate these capabilities; first, an analysis of a coverage-dependent phase diagram of absorbate NO on the Pt 3 Sn(111) terrace surface, and second, an investigation of adsorption energies, together with identifying unique minimum energy configurations, for the reaction intermediate propyne (CHCCH 3 *) adsorbed on a PdIn(021) step surface. The evolutionary algorithm approach reproduces high coverage configurations of NO on Pt 3 Sn(111) using only 15% of the number of simulations required for a brute force approach. Furthermore, the screening of potentially hundreds of multidentate adsorbates is shown to be possible without human intervention. The strategy presented is quite general and can be applied to a spectrum of complex atomic systems.
36 MATERIALS SCIENCE↗
Predicting Band-Gap of Inorganic Materials Using Neuromorphic Graph Learning
Predicting properties of inorganic materials is a heavily researched topic, with several new prediction approaches emerging as competitors. One such competitor is graph neural networks, which leverage the structure of the graph to aid in the prediction process. In this work, we propose integration of neuromorphic computation into the graph neural network pipeline. We call this approach Neuromorphic Graph Learning (NGL). We utilize the NGL approach to leverage evolutionary algorithms and a novel Spike Pipeline for Raster Analysis (SPIRE) for the prediction of band gap in inorganic materials.
Mulet, Ian [University of Tennessee (UT)]↗
Decentralized Collaborative Learning with Probabilistic Data Protection
We discuss future directions of Blockchain as a collaborative value co-creation platform, in which network participants can gain extra insights that cannot be accessed when disconnected from the others. As such, we propose a decentralized machine learning framework that is carefully designed to respect the values of democracy, diversity, and privacy. Specifically, we propose a federated multi-task learning framework that integrates a privacy-preserving dynamic consensus algorithm. We show that a specific network topology called the expander graph dramatically improves the scalability of global consensus building. We conclude the paper by making some remarks on open problems.
Ide, Tsuyoshi↗
ARCH: Large-scale knowledge graph via aggregated narrative codified health records analysis
Objective: Electronic health record (EHR) systems contain a wealth of clinical data stored as both codified data and free-text narrative notes (NLP). The complexity of EHR presents challenges in feature representation, information extraction, and uncertainty quantification. Here, to address these challenges, we proposed an efficient Aggregated naRrative Codified Health (ARCH) records analysis to generate a large-scale knowledge graph (KG) for a comprehensive set of EHR codified and narrative features. Methods: Using data from 12.5 million Veterans Affairs patients, ARCH first derives embedding vectors and generates similarities along with associated p-values to measure the strength of relatedness between clinical features with statistical certainty quantification. Next, ARCH performs a sparse embedding regression to remove indirect linkage between features to build a sparse KG. Finally, ARCH was validated on various clinical tasks, including detecting known relationships between entity pairs, predicting drug side effects, disease phenotyping, as well as sub-typing Alzheimer’s disease patients. Results: ARCH produces high-quality clinical embeddings and KG for over 60,000 codified and narrative EHR concepts. The KG and embeddings are visualized in the R-shiny powered web-API.3 ARCH achieved high accuracy in detecting EHR concept relationships, with AUCs of 0.926 (codified) and 0.861 (NLP) for similar EHR concepts, and 0.810 (codified) and 0.843 (NLP) for related pairs. It detected drug side effects with a 0.723 AUC, which improved to 0.826 after fine-tuning. Using both codified and NLP features, the detection power increased significantly. Compared to other methods, ARCH has superior accuracy and enhances weakly supervised phenotyping algorithms’ performance. Notably, it successfully categorized Alzheimer’s patients into two subgroups with varying mortality rates. Conclusion: The proposed ARCH algorithm generates large-scale high-quality semantic representations and knowledge graph for both codified and NLP EHR features, useful for a wide range of predictive modeling tasks.
Electronic health records↗
Finding Your Niche: An Evolutionary Approach to HPC Topologies
Traditional interconnection network design approaches focus on building general network topologies by optimizing the bisection bandwidth or minimizing the network’s diameter to reduce the maximum distance between any two nodes, thus amortizing the overall execution time of the HPC workloads. While such network topologies may accommodate a wide variety of applications in general, this may result in sub-optimal performance for many frequently-executed or dynamic workloads. In this paper, instead of focusing on designing an all-encompassing, general-purpose network topology, we develop a methodology to design customized network interconnects, evolved by “finding” the optimal topologies for a particular target workload given by its communication and contention profiles. To this end, we implement a Genetic Algorithm (GA)-based approach for network topology design tailored to improve the overall execution time of a particular workload of interest. We conducted extensive experiments with well-known motifs in physics-based workloads (Sweep3D and FFT), as well as with a representative graph application (MiniVite), using the well-known Structural Simulation Toolkit (SST) Macroscale Element Library (SST/macro) simulator for network interconnect evaluation. We demonstrate that our genetic algorithm-based approach is robust enough to find the underlying optimal topology of a particular workload.
network interconnects, graph search, meta-heuristi↗
Spectral Clustering-Based Partitioning of Large-Scale Power Electronics-Based Power Systems for Small-Signal Stability Analysis
The nodal admittance matrix (NAM)-based approach is well-suited for small-signal stability analysis of large-scale power electronics-based power systems (PEPSs), as it preserves the system structure through its admittance matrix. Previous studies have explored partitioning such systems into subareas and interconnections to reduce computational burden; however, they lacked a formal algorithmic procedure for determining feasible partitions. While several grid partitioning methods, such as those based on graph theory or machine learning, exist in the literature, they cannot be directly applied to NAM-based analysis due to differing objectives and constraints. Here, this paper addresses this gap by presenting a systematic, step-by-step procedure for applying a spectral partitioning algorithm that yields a division of the system into subareas suitable for NAM-based analysis. The computational complexity of the proposed method is also derived to demonstrate its efficiency and justify the practicality of the resulting subarea decomposition. The performance of the partitioning method is evaluated by applying the spectral clustering-derived subareas and interconnections to the NAM-based partitioning approach on a 140-bus system. Computational times for the full-system and partitioned NAM analyses are compared using MATLAB. Additionally, PSCAD simulations of the complete system and partitioned subareas are carried out to verify the effectiveness of the proposed method.
Nupur [Univ. of Tennessee, Knoxville, TN (United S↗
Scalable training of trustworthy and energy-efficient predictive graph foundation models for atomistic materials modeling: a case study with HydraGNN
We present our work on developing and training scalable, trustworthy, and energy-efficient predictive graph foundation models (GFMs) using HydraGNN, a multi-headed graph convolutional neural network architecture. HydraGNN expands the boundaries of graph neural network (GNN) computations in both training scale and data diversity. It abstracts over message passing algorithms, allowing both reproduction of and comparison across algorithmic innovations that define nearest-neighbor convolution in GNNs. This work discusses a series of optimizations that have allowed scaling up the GFMs training to tens of thousands of GPUs on datasets consisting of hundreds of millions of graphs. Our GFMs use multitask learning (MTL) to simultaneously learn graph-level and node-level properties of atomistic structures, such as energy and atomic forces. Using over 154 million atomistic structures for training, we illustrate the performance of our approach along with the lessons learned on two state-of-the-art US Department of Energy (US-DOE) supercomputers, namely the Perlmutter petascale system at the National Energy Research Scientific Computing Center and the Frontier exascale system at Oak Ridge Leadership Computing Facility. The HydraGNN architecture enables the GFM to achieve near-linear strong scaling performance using more than 2000 GPUs on Perlmutter and 16,000 GPUs on Frontier.
97 MATHEMATICS AND COMPUTING↗
Semi-supervised graph neural networks for pileup noise removal
Abstract The high instantaneous luminosity of the CERN Large Hadron Collider leads to multiple proton–proton interactions in the same or nearby bunch crossings (pileup). Advanced pileup mitigation algorithms are designed to remove this noise from pileup particles and improve the performance of crucial physics observables. This study implements a semi-supervised graph neural network for particle-level pileup noise removal, by identifying individual particles produced from pileup. The graph neural network is firstly trained on charged particles with known labels, which can be obtained from detector measurements on data or simulation, and then inferred on neutral particles for which such labels are missing. This semi-supervised approach does not depend on the neutral particle pileup label information from simulation, and thus allows us to perform training directly on experimental data. The performance of this approach is found to be consistently better than widely-used domain algorithms and comparable to the fully-supervised training using simulation truth information. The study serves as the first attempt at applying semi-supervised learning techniques to pileup mitigation, and opens up a new direction of fully data-driven machine learning pileup mitigation studies.
43 PARTICLE ACCELERATORS↗