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DOE OSTI2023

Comparative Study of Variations in Quantum Approximate Optimization Algorithms for the Traveling Salesman Problem

The traveling salesman problem (TSP) is one of the most often-used NP-hard problems in computer science to study the effectiveness of computing models and hardware platforms. In this regard, it is also heavily used as a vehicle to study the feasibility of the quantum computing paradigm for this class of problems. In this paper, we tackle the TSP using the quantum approximate optimization algorithm (QAOA) approach by formulating it as an optimization problem. By adopting an improved qubit encoding strategy and a layer-wise learning optimization protocol, we present numerical results obtained from the gate-based digital quantum simulator, specifically targeting TSP instances with 3, 4, and 5 cities. We focus on the evaluations of three distinctive QAOA mixer designs, considering their performances in terms of numerical accuracy and optimization cost. Notably, we find that a well-balanced QAOA mixer design exhibits more promising potential for gate-based simulators and realistic quantum devices in the long run, an observation further supported by our noise model simulations. Furthermore, we investigate the sensitivity of the simulations to the TSP graph. Overall, our simulation results show that the digital quantum simulation of problem-inspired ansatz is a successful candidate for finding optimal TSP solutions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Scalable edge clustering of dynamic graphs via weighted line graphs

Timestamped relational datasets consisting of records (or connections) between pairs of entities are ubiquitous in network science. For applications like peer-to-peer communication, email, various social network interactions, and computer network security, it is useful to organize these records into groups based on how and when they are occurring. Weighted line graphs offer a natural way to model how records are related in such datasets but for large real-world graph topologies, building and utilizing the line graph is prohibitively expensive. Here, we present the framework to cluster the edges of a dynamic graph via the associated line graph that contains two major contributions. The first is a method to work with the line graph implicitly and the second is a distributed scale implementation of an agglomerative hierarchical graph clustering algorithm. We outline a novel hierarchical dynamic graph edge clustering approach that efficiently breaks massive relational datasets into small sets of edges containing events at various timescales. This is in stark contrast to traditional graph clustering algorithms that prioritize highly connected (clique-like) community structures. Our approach relies on constructing a sufficient subgraph of a weighted line graph and applying a hierarchical agglomerative clustering. This approach is related to scalable techniques from spatial clustering, nonlinear-dimension reduction, topological data analysis, and draws particular inspiration from HDBSCAN. As an edge clustering, this method yields an overlapping node clustering. Our algorithm is parallelizable and we demonstrate efficient clustering of a billion-scale, real-world dynamic graph into small edge sets that correlate in topology and time. The entire clustering process for a graph with tens of billions of edges takes just a few minutes of run time on 256 nodes of a distributed compute environment. We argue how the output of the edge clustering is useful for a multitude of data visualization and powerful machine learning tasks, both involving the original massive dynamic graph data and metadata associated with the nodes and edges. Finally, we describe how this approach can be extended to dynamic hypergraphs and dynamic graphs/hypergraphs with unstructured data living on vertices and edges.

Data Analysis↗

DOE OSTI2019

Exploring MPI Communication Models for Graph Applications Using Graph Matching as a Case Study

Traditional implementations of parallel graph operations on distributed memory platforms are written using Message Passing Interface (MPI) point to point communication primitives such as Send-Recv (blocking and nonblocking). Apart from this classical model, the MPI community has over the years added other communication models; however, their suitability for handling the irregular traffic workloads typical of graph operations remain comparatively less explored. Our aim in this paper is to study these relatively underutilized communication models of MPI for graph applications. More specifically, we evaluate MPI’s one-sided programming, or Remote Memory Access (RMA), and nearest neighborhood collectives using a process graph topology. There are features in these newer models that are intended to better map to irregular communication patterns, as exemplified in graph algorithms. As a concrete application for our case study, we use distributed memory implementations of a weighted graph matching algorithm to investigate performances of MPI-3 RMA and neighborhood collective operations compared to nonblocking Send- Recv. A matching in a graph is a subset of edges such that no two matched edges are incident on the same vertex. A maximum weight matching is a matching of maximum weight computed as the sum of the weights of matched edges. Algorithms for optimal matching have quadratic complexity and are difficult to parallelize. More importantly, execution of graph matching is dominated by high volume of irregular memory accesses, making it an ideal candidate for studying the effects of various MPI communication models on graph applications at scale. Our neighborhood collectives and RMA implementations yields up to 6× speedup over traditional optimized nonblocking Send-Recv implementations, on thousands of cores of the NERSC Cori supercomputer. We believe the lessons learned from this case study can be adopted to benefit a wider range of graph application codes.

Ghosh, Sayan↗

DOE OSTI2025

Impact of Domain Knowledge on the Property Prediction of Specialized Machine Learning Models

Developing transferable machine learning models is trending in data-driven materials research. However, how to apply such models to a specific research domain remains unclear. Here, in this work, we choose high-entropy materials as a platform with a specialized data set containing 145,323 DFT-relaxed materials. This data set is used to explore the role of domain-specific knowledge in training effective models. Our tests with three representative graph neural network architectures indicate the model complexity has much smaller influence on performance than the data itself. Specifically, the consideration of low-energy atomic ordering, structures with diverse elemental coverage, and high-order interactions significantly influences the model performance. We also find that domain knowledge-driven sampling can greatly enhance unsupervised learning techniques. This research highlights that developing specialized data sets is more beneficial than further complicating deep learning architectures. Additionally, physics-inspired sampling algorithms are crucially needed for better machine learning models for a specific materials research domain.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Development of Multimodal Few-Shot Analytics for Electron Micrographs

Recent advances in materials data analytics have provided new avenues for determining process-structure-property (PSP) linkages in a variety of materials. Machine learning techniques including few-shot learning have increased the efficiency of classifying microscopy images for the purposes of material characterization. Attempts at creating a multimodal approach can provide further improvements to current models and help extract more salient features from data. In this vein, raw spectrum data was taken to provide an additional modality to our current pyCHIP classifier. Modifications in segmentation also show potential in improving the accuracy of the pyCHIP classifier. Classifier output was analyzed using network graphs and unsupervised clustering algorithms such as spectral clustering to detect better segmentation methods than the current “chipping” approach. We suggest that the chip selection process can be automated in the future using a combination of these techniques to enable high-throughput analyses.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A Two-Stage Quantum Reinforcement Learning Method for Multi-Objective Transmission Switching

Multi-objective transmission switching (MO-TS) problems involve the strategic reconfiguration of network topology to simultaneously optimize multiple objectives. As the system scale increases, finding feasible solutions becomes increasingly challenging due to the problem's nonlinearity and high computational complexity. To address these challenges, this paper proposes a two-stage quantum reinforcement learning method that leverages potential quantum advantages for MO-TS. In the first stage, candidate switching lines are identified using a graph-theoretical approach to reduce the problem's dimensionality. The second stage introduces a quantum-classical reinforcement learning framework, where a learnable measurement-based CNN-ResVQC architecture is developed to effectively reduce the input dimension for quantum processing, mitigate vanishing gradients, and enhance trainability while improving the quantum circuit's flexibility in modeling complex decision policies for MO-TS. Numerical studies on IEEE 14-bus, 57-bus, and 118-bus systems demonstrate that the proposed algorithm achieves superior training stability and faster convergence with approximately 1% of the network parameters required by classical algorithms, highlighting its effectiveness, efficiency, and scalability. Furthermore, the practicality is validated through its stable convergence under three common quantum noise channels.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2021

Universal image representation based on a multimodal graph

A system for classifying a target image with segments having attributes is provided. The system generates a graph for the target image that includes vertices representing segments of the image and edges representing relationships between the connected vertices. For each vertex, the system generates a subgraph that includes the vertex as a home vertex and neighboring vertices representing segments of the target image within a neighborhood of the segment represented by the home vertex. The system applies an autoencoder to each subgraph to generate latent variables to represent the subgraph. The system applies a machine learning algorithm to a feature vector comprising a universal image representation of the target image that is derived from the generated latent variables of the subgraphs to generate a classification for the target image.

Bremer, Peer-Timo↗

DOE OSTI2023

Universal image representation based on a multimodal graph

Bremer, Peer-Timo↗

DOE OSTI2023

Trigger Detection for the sPHENIX Experiment via Bipartite Graph Networks with Set Transformer

Trigger (interesting events) detection is crucial to high-energy and nuclear physics experiments because it improves data acquisition efficiency. It also plays a vital role in facilitating the downstream offline data analysis process. The sPHENIX detector, located at the Relativistic Heavy Ion Collider in Brookhaven National Laboratory, is one of the largest nuclear physics experiments on a world scale and is optimized to detect physics processes involving charm and beauty quarks. Furthermore, these particles are produced in collisions involving two proton beams, two gold nuclei beams, or a combination of the two and give critical insights into the formation of the early universe. This paper presents a model architecture for trigger detection with geometric information from two fast silicon detectors. Transverse momentum is introduced as an intermediate feature from physics heuristics. We also prove its importance through our training experiments. Each event consists of tracks and can be viewed as a graph. A bipartite graph neural network is integrated with the attention mechanism to design a binary classification model. Compared with the state-of-the-art algorithm for trigger detection, our model is parsimonious and increases the accuracy and the AUC score by more than 15%.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

A General Spatiotemporal Imputation Framework for Missing Sensor Data

Many applications from precision agriculture, environmental monitoring and transportation networks rely on data collected across space and time over a large geographic area. Missing data poses a significant challenge for any data-driven inference and control tasks. Data imputation or the estimation of missing data can help fill these gaps by utilizing inherent spatial relationships and temporal patterns. A variety of spatiotemporal imputation models have been developed to address missing data in spatiotemporal datasets. However, these classical methods rely on the assumption that the underlying data follows a smooth trend and fail to provide accurate estimates when there is a large number of missing points in the data. Even though there are machine learning driven tensor completion approaches such as convolutional neural network based tensor completion (CoSTCo) that capture the non-linear relationships in the dataset, the transductive nature makes the algorithm less scalable. Thus, existing approaches for estimating the missing information do not effectively capture all dimensions of the spatiotemporal data structure, resulting in erroneous predictions and poor performance. The main contributions of this paper are: (1) We propose a novel inductive framework (G-LSTM) for missing data imputation that integrates a graph neural network with LSTMs to effectively capture both spatial and temporal dependencies. (2) Experimental results on a traffic dataset demonstrate that the proposed GNN integrated with an LSTM framework achieves improved imputation and maintains steady performance even when there are extreme missing conditions in comparison with the state-of-the-art imputation framework (i.e, CoSTCo). (3) The simulation results on a traffic network show up to 69% reduction in mean absolute error and 61% reduction in root mean square error when compared to CoSTCo.

Tharzeen, Aabila↗

DOE OSTI2024

Scaling whole-chip QAOA for higher-order ising spin glass models on heavy-hex graphs

Abstract We show that the quantum approximate optimization algorithm (QAOA) for higher-order, random coefficient, heavy-hex compatible spin glass Ising models has strong parameter concentration across problem sizes from 16 up to 127 qubits for p = 1 up to p = 5, which allows for computationally efficient parameter transfer of QAOA angles. Matrix product state (MPS) simulation is used to compute noise-free QAOA performance. Hardware-compatible short-depth QAOA circuits are executed on ensembles of 100 higher-order Ising models on noisy IBM quantum superconducting processors with 16, 27, and 127 qubits using QAOA angles learned from a single 16-qubit instance using the JuliQAOA tool. We show that the best quantum processors find lower energy solutions up to p = 2 or p = 3, and find mean energies that are about a factor of two off from the noise-free distribution. We show that p = 1 QAOA energy landscapes remain very similar as the problem size increases using NISQ hardware gridsearches with up to a 414 qubit processor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Data Summarization and Inference at Scale

This is the final report for the DOE ASCR grant SC-0022260, Data Summarization and Inference at Scale, PI: Alex Pothen, Purdue University. The goal of the project was to solve data-intensive and compute-intensive problems in the physical sciences, engineering, information science, data science, etc. by designing and implementing new algorithms that could work with a subset of the data. The four subgoals were: (a) The solution of problems where the data is too large to be stored in the memory of a computer. In this streaming model of computation, the data arrives as a stream of elements to the computer, each element is processed as it arrives, and a decision is made to discard the data or to store it; only a small subset of the data proportional to the size of the output solution is stored, and when all the data has been streamed, a solution to the problem is computed from the stored subset. (b) The use of machine learning methods to compute solutions to data-intensive problems. The use of GPUs is critical to obtain high performance on machine learning tasks, but their memory sizes are smaller relative to that of CPUs. For large-scale problems, the data is sampled many times, and small samples are used with repetition, for robustness, to compute solutions to inference tasks. This sampling reduces the memory required to solve the problem, but attention is needed to avoid slow convergence to the solutions, and reduced accuracy of inference. We propose submodular optimization, Large Language Models, and physics-informed neural networks to enable GPU computations here. (c) Modeling and visualization of high-dimensional data using interpretable features. Clinical proteomic data sets from immunology for the detection of cancer and other diseases are temporal and high-dimensional, and algorithms for visualizing these data sets using clinically interpretable features are lacking. We propose methods that compute distances based on the optimal transportation problem and graph edit distances to address this problem. We also propose the use of optimal transport-based distances, spatial statistics, and network structure to classify image data sets, We apply these algorithms to electron micrographs of the peripheral nervous system in the digestive tract. (d) The design of data-intensive algorithms on emerging architectures, specifically, noisy, intermediate-scale quantum (NISQ) devices. Quantum computers offer the possibility of exploring large solution spaces due to the principle of superposition, but current quantum computers are limited by few qubits, short coherence times due to noise, poor interconections among the qubits, etc. We propose the use of the divide and conquer paradigm to solve large-scale problems, wherein collections of small subproblems are solved on the quantum devices, and the solutions to the subproblems are integrated into a solution for the original problem on a classical computer.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

The Analysis Description Language Ecosystem: Latest developments and physics applications

We present latest developments in Analysis Description Language (ADL), a declarative domain-specific language describing the physics algorithm of a HEP data analysis decoupled from software frameworks. Analyses written in ADL can be integrated into any framework for various tasks. ADL is a multipurpose construct with uses ranging from analysis design to preservation, reinterpretation, queries, visualisation, combination, etc. The most advanced infrastructure to execute ADL on events is the CutLang runtime interpreter. Recent technical developments include an automated interface with different data types, generation of the abstract syntax tree, a visualization tool that that auto-converts analysis flows to graphs, incorporation of trained machine learning models and a Jupyter-based plotting tool. We also report physics implications including a large scale LHC analysis implementation and validation effort for beyond the standard model reinterpretation purposes and studies with ATLAS and CMS open data.

Sekmen, Sezen [Kyungpook National Univ., Daegu (Ko↗

DOE OSTI2025

Enabling Efficient Sparse Computations using Linear Algebra Aware Compilers

This project developed the LAPIS compiler framework, built on the Multilevel Intermediate Representation (MLIR), to optimize sparse linear algebra operations and support performance portability across diverse architectures. The main innovation of LAPIS is the Kokkos dialect, which allows for lowering codes from a high productivity language to different architectures in an elegant way. The dialect also allows the conversion of lower-level MLIR code to C++ Kokkos code, facilitating the integration of scientific machine learning (SciML) models into applications. To extend LAPIS for distributed memory architectures, a new partition dialect was created to manage the distribution of sparse tensors and express communication patterns for sparse linear algebra operations. This dialect also supports the distributed execution of operators and includes algorithmic optimizations to minimize communication to improve performance. The project also demonstrates that MLIR can enable effective linear algebra-level optimizations, improving performance on different GPUs for both sparse and dense linear algebra kernels. Key applications of LAPIS include sparse linear algebra and graph kernels, TenSQL, a relational database management solution built on GraphBLAS, and the development of subgraph isomorphism and monomorphism kernels, showcasing performance portability. In summary, the LAPIS framework supports productivity, performance, portability, and distributed memory execution, while also enabling linear algebra-level optimizations that are challenging in traditional programming languages, with successful applications ranging from simple sparse linear algebra to complex graph kernels.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

FAIR AI models in high energy physics

Abstract The findable, accessible, interoperable, and reusable (FAIR) data principles provide a framework for examining, evaluating, and improving how data is shared to facilitate scientific discovery. Generalizing these principles to research software and other digital products is an active area of research. Machine learning models—algorithms that have been trained on data without being explicitly programmed—and more generally, artificial intelligence (AI) models, are an important target for this because of the ever-increasing pace with which AI is transforming scientific domains, such as experimental high energy physics (HEP). In this paper, we propose a practical definition of FAIR principles for AI models in HEP and describe a template for the application of these principles. We demonstrate the template’s use with an example AI model applied to HEP, in which a graph neural network is used to identify Higgs bosons decaying to two bottom quarks. We report on the robustness of this FAIR AI model, its portability across hardware architectures and software frameworks, and its interpretability.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms

The emergent practical applicability of the Quantum Approximate Optimization Algorithm (QAOA) for approximate combinatorial optimization is a subject of considerable interest. One of the primary limitations of QAOA is the task of finding a set of good parameters, which is usually done using a variational optimization loop. Parameter transfer, or parameter concentration, is a phenomenon where QAOA angles trained on problem instances that are self-similar tend to perform well for other problem instances from that similar class. This suggests a potentially highly efficient and scalable non-variational learning method for QAOA angle finding. In this work, we systematically study QAOA parameter transferability from small problem sizes (16 and 27 decision variables) onto large problem instances (up to 156 qubits) for heavy-hex graph Ising models with geometrically local higher order terms using the Julia based QAOA simulation tool \texttt{JuliQAOA} to perform classical angle finding for up to $49$ QAOA layers ($p$). Parameter transfer of the fixed angles is validated using a combination of full statevector, Projected Entangled Pair States (PEPS), Matrix Product State (MPS), and LOWESA numerical simulations. We find that the QAOA parameter transfer from single instances applied to other (unseen) problem instances does not in general provide monotonically improving performance as a function of $p$ - there are many cases where the performance temporarily decreases as a function of $p$ - but despite this the transferred angles have a general trend of improved expectation value as the QAOA depth increases, in many cases converging close to the true ground-state energy of the $100+$ qubit instances. We also sample the hardware-compatible Ising models using the ensemble of transfer-learned QAOA parameters on several superconducting qubit IBM Quantum processors with 127, 133, and 156 qubits. We find continuous solution quality improvement of the hardware-compatible QAOA circuits run on the IBM NISQ processors up to $p=5$ on \texttt{ibm\_fez}, up to $p=9$ on \texttt{ibm\_torino}, and up to $p=10$ on \texttt{ibm\_pittsburgh}.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Direction-optimizing Label Propagation and its Application for Community Detection

Label Propagation is a machine learning algorithm typically used for classification. It has also been found to be an effective method for detecting communities in networks. It has two attractive features as a community detection method: it has nearly linear runtime and it requires no \textit{a priori} community information. We propose a new Direction Optimizing Label Propagation Algorithm (DOLPA) that relies on the use of {\em frontiers} and alternates between label {\em push} and label {\em pull} operations to enhance the performance of LPA. Specifically, DOLPA has parameters for tuning the processing order of vertices in a graph. This reduces the number of edges visited and improves the quality of solution. We apply DOLPA to community detection and present the design and implementation of the algorithm as well as its shared-memory parallelization using OpenMP. Empirically, we evaluate our algorithm using synthetic graphs as well as real-world networks. Compared with the state-of-art \textit{Parallel Label Propagation} algorithm, we achieve at least two times the F-Score while reducing the runtime by 50\% for synthetic graphs with overlapping communities. We also compare DOLPA against the state-of-art parallel implementation of the Louvain method using the same graphs and show that DOLPA achieves about three times the F-Score at 10\% the runtime. On real-world graphs, we get a speedup of up to $10\times$ using 64 threads.

Liu, X↗

DOE OSTI2024

Cluster expansion by transfer learning for phase stability predictions

Recent progress towards universal machine-learned interatomic potentials holds considerable promise for materials discovery. Yet the accuracy of these potentials for predicting phase stability may still be limited. In contrast, cluster expansions provide accurate phase stability predictions but are computationally demanding to parameterize from first principles, especially for structures of low dimension or with a large number of components, such as interfaces or multimetal catalysts. We overcome this trade-off via transfer learning. Using Bayesian inference, we incorporate prior statistical knowledge from machine-learned and physics-based potentials, enabling us to sample the most informative configurations and to efficiently fit first-principles cluster expansions. Furthermore, this algorithm is tested on Pt:Ni, showing robust convergence of the mixing energies as a function of sample size with reduced statistical fluctuations.

36 MATERIALS SCIENCE↗