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DOE OSTI2023

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↗

DOE OSTI2025

CAMEO: A Co-design Architecture for Multi-objective Energy System Optimization (Project Report)

CAMEO (Codesign Architecture for Multi-objective Energy System Optimization) is a modular workflow management framework that abstracts co-design problems as Directed Acyclic Graphs (DAG). The framework employs JSON-based workflow specifications that enable systematic decomposition of complex optimization problems into reusable, interchangeable components including data loaders, scenario generators, optimization solvers, and result summarizers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Solving larger maximum clique problems using parallel quantum annealing

Quantum annealing has the potential to find low energy solutions of NP-hard problems that can be expressed as quadratic unconstrained binary optimization problems. However, the hardware of the quantum annealer manufactured by D-Wave Systems, which we consider in this work, is sparsely connected and moderately sized (on the order of thousands of qubits), thus necessitating a minor-embedding of a logical problem onto the physical qubit hardware. The combination of relatively small hardware sizes and the necessity of a minor-embedding can mean that solving large optimization problems is not possible on current quantum annealers. In this research, we show that a hybrid approach combining parallel quantum annealing with graph decomposition allows one to solve larger optimization problem accurately. We apply the approach to the Maximum Clique problem on graphs with up to 120 nodes and 6395 edges.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Impact of graph structures for QAOA on MaxCut

The quantum approximate optimization algorithm (QAOA) is a promising method of solving combinatorial optimization problems using quantum computing. QAOA on the MaxCut problem has been studied extensively on graphs with specific structure; however, little is known about the general performance of the algorithm on arbitrary graphs. Here, we investigate how different graph characteristics correlate with QAOA performance at depths at most three on the MaxCut problem for all connected non-isomorphic graphs with at most eight vertices. Some good predictors of QAOA success relate to graph symmetries, odd cycles, and density. For example, on eight vertex graphs, the average probability for selecting an optimal solution for graphs that contain no odd cycles after three iterations of QAOA is 60.6% compared to 48.2% for those that do. The data generated from these studies are shared in a publicly accessible database to serve as a benchmark for QAOA calculations and experiments. Knowing the relationship between structure and performance can be used to identify classes of combinatorial problems that are likely to exhibit a quantum advantage.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Preventing Failures By Dataset Shift Detection in Safety-Critical Graph Applications

Dataset shift refers to the problem where the input data distribution may change over time (e.g., between training and test stages). Since this can be a critical bottleneck in several safety-critical applications such as healthcare, drug-discovery, etc., dataset shift detection has become an important research issue in machine learning. Though several existing efforts have focused on image/video data, applications with graph-structured data have not received sufficient attention. Therefore, in this paper, we investigate the problem of detecting shifts in graph structured data through the lens of statistical hypothesis testing. Specifically, we propose a practical two-sample test based approach for shift detection in large-scale graph structured data. Our approach is very flexible in that it is suitable for both undirected and directed graphs, and eliminates the need for equal sample sizes. Using empirical studies, we demonstrate the effectiveness of the proposed test in detecting dataset shifts. We also corroborate these findings using real-world datasets, characterized by directed graphs and a large number of nodes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Machine-learning-aided cognitive reconfiguration for flexible-bandwidth HPC and data center networks [Invited]

This paper proposes a machine-learning (ML)-aided cognitive approach for effective bandwidth reconfiguration in optically interconnected datacenter/high-performance computing (HPC) systems. The proposed approach relies on a Hyper-X-like architecture augmented with flexible-bandwidth photonic interconnections at large scales using a hierarchical intra/inter-POD photonic switching layout. We first formulate the problem of the connectivity graph and routing scheme optimization as a mixed-integer linear programming model. A two-phase heuristic algorithm and a joint optimization approach are devised to solve the problem with low time complexity. Then, we propose an ML-based end-to-end performance estimator design to assist the network control plane with intelligent decision making for bandwidth reconfiguration. Numerical simulations using traffic distribution profiles extracted from HPC applications traces as well as random traffic matrices verify the accuracy performance of the ML design estimator ( < <#comment/> 9 % <#comment/> error) and demonstrate up to 5 × <#comment/> throughput gain from the proposed approach compared with the baseline Hyper-X network using fixed all-to-all intra/inter-portable data center interconnects.

Chen, Xiaoliang (ORCID:0000000278056237)↗

DOE OSTI2025

Quantum Adiabatic Optimization with Rydberg Arrays: Localization Phenomena and Encoding Strategies

Quantum adiabatic optimization seeks to solve combinatorial problems using quantum dynamics, requiring the Hamiltonian of the system to align with the problem of interest. However, these Hamiltonians are often incompatible with the native constraints of quantum hardware, necessitating encoding strategies to map the original problem into a hardware-conformant form. While the classical overhead associated with such mappings is easily quantifiable and typically polynomial in problem size, it is much harder to quantify their overhead on the quantum algorithm, e.g., the transformation of the adiabatic timescale. In this work, we address this challenge on the concrete example of the encoding scheme proposed in [Nguyen , PRX Quantum , 010316 (2023)], which is designed to map optimization problems on arbitrarily connected graphs into Rydberg atom arrays. We consider the fundamental building blocks underlying this encoding scheme and determine the scaling of the minimum gap with system size along adiabatic protocols. Even when the original problem is trivially solvable, we find that the encoded problem can exhibit an exponentially closing minimum gap. We show that this originates from a quantum coherent effect, which gives rise to an unfavorable localization of the ground-state wave function. On the QuEra Aquila neutral atom machine, we observe such localization and its effect on the success probability of finding the correct solution to the encoded optimization problem. Finally, we propose quantum-aware modifications of the encoding scheme that avoid this quantum bottleneck and lead to an exponential improvement in the adiabatic performance. This highlights the crucial importance of accounting for quantum effects when designing strategies to encode classical problems onto quantum platforms. Published by the American Physical Society 2025

Bombieri, Lisa (ORCID:0009000950422897)↗

DOE OSTI2024

4-Clique network minor embedding for quantum annealers

Quantum annealing is a quantum algorithm for computing solutions to combinatorial optimization problems. This study proposes a method for minor embedding optimization problems onto sparse quantum annealing hardware graphs called 4-clique network minor embedding. This method is in contrast to the standard minor embedding technique of using a path of linearly connected qubits in order to represent a logical variable state. The 4-clique minor embedding is possible on Pegasus graph connectivity, which is the native hardware graph for some of the current D-Wave quantum annealers. The Pegasus hardware graph contains many cliques of size 4, making it possible to form a graph composed entirely of paths of connected 4-cliques on which a problem can be minor-embedded. The 4-clique chains come at the cost of additional qubit usage on the hardware graph, but they allow for stronger coupling within each chain, thereby increasing chain integrity, reducing chain breaks, and allow for greater usage of the available energy scale for programming logical problem coefficients on current quantum annealers. The 4-clique minor embedding technique is compared with the standard linear path minor embedding with experiments on two D-Wave quantum annealing processors with Pegasus hardware graphs. We show proof-of-concept experiments where the 4-clique minor embeddings can use weak chain strengths while successfully carrying out the computation of minimizing random all-to-all spin glass problem instances. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Classical combinatorial optimization scaling for random Ising models on 2D heavy-hex graphs

Motivated by near term quantum computing hardware limitations, combinatorial optimization problems that can be addressed by current quantum algorithms and noisy hardware with little or no overhead are used to probe capabilities of quantum algorithms such as the quantum approximate optimization algorithm. In this study, a specific class of near term quantum computing hardware defined combinatorial optimization problems, Ising models on heavy-hex graphs both with and without geometrically local cubic terms, are examined for their classical computational hardness via empirical computation time scaling quantification. Specifically the time-to-solution (TTS) metric using the classical heuristic simulated annealing is measured for finding optimal variable assignments (ground states), as well as the time required for the optimization software Gurobi to find an optimal variable assignment. Because of the sparsity of these Ising models, the classical algorithms are able to find optimal solutions efficiently even for large instances (i.e. 100 000 spin variables). The Ising models both with and without geometrically local cubic terms exhibit average-case linear-time or weakly quadratic scaling when solved exactly using Gurobi, and the Ising models with no cubic terms show evidence of exponential-time TTS scaling when sampled using simulated annealing. These findings point to the necessity of developing and testing more complex, namely more densely connected, optimization problems in order for quantum computing to ever have a practical advantage over classical computing. Our results are another illustration that different classical algorithms can indeed have exponentially different running times, thus making the identification of the best practical classical technique important in any quantum computing vs. classical computing comparison.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Entanglement perspective on the quantum approximate optimization algorithm

Many quantum algorithms seek to output a specific bitstring solving the problem of interest—or a few if the solution is degenerate. It is the case for the quantum approximate optimization algorithm (QAOA) in the limit of large circuit depth, which aims to solve quadratic unconstrained binary optimization problems. Hence, the expected final state for these algorithms is either a product state or a low-entangled superposition involving a few bitstrings. What happens in between the initial N -qubit product state | 0 〉 ⊗ N and the final one regarding entanglement? Here, we consider the QAOA algorithm for solving the paradigmatic MaxCut problem on different types of graphs. We study the entanglement growth and spread resulting from randomized and optimized QAOA circuits and find that there is a volume-law entanglement barrier between the initial and final states. We also investigate the entanglement spectrum in connection with random matrix theory. In addition, we compare the entanglement production with a quantum annealing protocol aiming to solve the same MaxCut problems. Finally, we discuss the implications of our results for the simulation of QAOA circuits with tensor network-based methods relying on low-entanglement for efficiency, such as matrix product states.

Dupont, Maxime↗

DOE OSTI2023

Automated Adversary-in-the-Loop Cyber-Physical Defense Planning

Security of cyber-physical systems (CPS) continues to pose new challenges due to the tight integration and operational complexity of the cyber and physical components. To address these challenges, this article presents a domain-aware, optimization-based approach to determine an effective defense strategy for CPS in an automated fashion—by emulating a strategic adversary in the loop that exploits system vulnerabilities, interconnection of the CPS, and the dynamics of the physical components. Our approach builds on an adversarial decision-making model based on a Markov Decision Process (MDP) that determines the optimal cyber (discrete) and physical (continuous) attack actions over a CPS attack graph. The defense planning problem is modeled as a non-zero-sum game between the adversary and defender. We use a model-free reinforcement learning method to solve the adversary’s problem as a function of the defense strategy. We then employ Bayesian optimization (BO) to find an approximate best-response for the defender to harden the network against the resulting adversary policy. This process is iterated multiple times to improve the strategy for both players. We demonstrate the effectiveness of our approach on a ransomware-inspired graph with a smart building system as the physical process. Numerical studies show that our method converges to a Nash equilibrium for various defender-specific costs of network hardening.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Graphical Gaussian Process Regression Model for Aqueous Solvation Free Energy Prediction of Organic Molecules in Redox Flow Battery

The solvation free energy of organic molecules is a critical parameter in determining emergent properties such as solubility, liquid-phase equilibrium constants, and pKa and redox potentials in an organic redox flow battery. In this work, we present a machine learning (ML) model that can learn and predict the aqueous solvation free energy of an organic molecule using Gaussian process regression method based on a new molecular graph kernel. To investigate the performance of the ML model on electrostatic interaction, the nonpolar interaction contribution of solvent and the conformational entropy of solute in solvation free energy, three data sets with implicit or explicit water solvent models, and contribution of conformational entropy of solute are tested. We demonstrate that our ML model can predict the solvation free energy of molecules at chemical accuracy with a mean absolute error of less than 1 kcal/mol for subsets of the QM9 dataset and the Freesolv database. To solve the general data scarcity problem for a graph-based ML model, we propose a dimension reduction algorithm based on the distance between molecular graphs, which can be used to examine the diversity of the molecular data set. It provides a promising way to build a minimum training set to improve prediction for certain test sets where the space of molecular structures is predetermined.

25 ENERGY STORAGE↗

DOE OSTI2025

Graph-Based Attention Mechanisms for Solving the AC Optimal Power Flow Problem in Electrical Power Networks

With the increasing complexity and data availability in modern power systems, learning-based approaches to AC Optimal Power Flow (AC OPF) have garnered significant attention. In particular, the structure of smart grids lends itself naturally to graph-based representations, where Graph Neural Networks (GNNs) can capture spatial and relational dependencies. This paper investigates attention-based GNN architectures tailored to heterogeneous graph representations of electric grids. We evaluate two major paradigms: relational attention, which distinguishes between edge types during message passing, and meta-path attention, which captures high-level semantics through multi-hop, typed paths. Using a large corpus of public AC OPF scenarios, we benchmark representative models of each type of attention. Our results demonstrate the benefits of heterogeneous attention-based models in accurately capturing grid dynamics; heterogeneous attention models achieve superior performance in both standard and perturbed settings. The findings highlight the importance of semantic-aware architectures for improving prediction robustness and interpretability in power system applications.

Trigui, Ali [Qubit Engineering Inc.]↗

DOE OSTI2025

Quantum graph learning and algorithms applied in quantum computer sciences and image classification

Graph and network theory play a fundamental role in quantum computer sciences, including quantum information and computation. Random graphs and complex network theory are pivotal in predicting novel quantum phenomena, where entangled links are represented by edges. Quantum algorithms have been developed to enhance solutions for various network problems, giving rise to quantum graph computing and quantum graph learning (QGL). Here, in this review, we explore graph theory and graph learning methods as powerful tools for quantum computers to generate efficient solutions to problems beyond the reach of classical systems. We delve into the development of quantum complex network theory and its applications in quantum computation, materials discovery, and research. We also discuss quantum machine learning (QML) methodologies for effective image classification using qubits, quantum gates, and quantum circuits. Additionally, the paper addresses the challenges of QGL and algorithms, emphasizing the steps needed to develop flexible QGL solvers. This review presents a comprehensive overview of the fields of QGL and QML, highlights recent advancements, and identifies opportunities for future research.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Fundamental Path Optimization Strategies for Extrusion-based Additive Manufacturing

Extrusion-based additive manufacturing processes begin with a software program, called a slicer, that generates layer geometry and fits toolpaths to each layer to define where material is to be extruded or deposited. Before the toolpaths are output as g-code for the additive manufacturing system to execute, the toolpaths should be optimized. Many complex optimization approaches using graph theory, Chinese postman problem, and other complex mathematical models exist, but these approaches are rarely used in daily printing operations and are not available through common slicing programs such as Cura and PrusaSlicer. Instead, path planning and optimization typically revolves around simpler, fully automated approaches such as inside out and next closest. This paper will explore the fundamental optimization strategies for toolpath planning and document a new implementation, available via open-source slicing software, that allows for greater control of the path planning process.

Roschli, Alex [ORNL] (ORCID:0000000213084632)↗

DOE OSTI2025

Benders Decomposition Using Graph Modeling and Multi-Parametric Programming

Benders decomposition is a widely used method for solving large and structured optimization problems, but its performance is affected by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating Benders decomposition. Specifically, we express the problem structure by using a graph-theoretic modeling abstraction in which nodes represent optimization subproblems and edges represent connectivity between subproblems. A key innovation of our approach is that we embed multiparametric programming (mp) surrogates for node subproblems, which maps the exact analytical map of the subproblem solution space. The use of mp surrogates allows us to replace subproblem solves with fast look-ups and function evaluations for primal and dual variables during the iterative Benders process. We formally show the equivalence between classical Benders cuts and those derived from the mp solution. We implement our framework in the open-source PlasmoBenders.jl software package. To demonstrate the capabilities of the proposed framework, we apply it to a two-stage stochastic programming problem, which aims to make optimal capacity expansion decisions under market uncertainty. We evaluate both single-cut and multicut variants of Benders decomposition and show that the use of mp surrogates achieves substantial speedups in subproblem solve time, while preserving the convergence guarantees of Benders decomposition. We highlight advantages in solution analysis and interpretability that is enabled by mp critical region tracking; specifically, we show that these reveal how decisions evolve geometrically across the Benders search. Our results aim to demonstrate that combining surrogate modeling with graph modeling offers a promising and extensible foundation for structure-exploiting decomposition. In addition, by decomposing the problem into more tractable subproblems, the proposed approach also aims to overcome scalability issues of mp. Finally, the use of mp surrogates provides a unifying and modular optimization framework that enables the representation of heterogeneous node subproblems as modeling objects with a homogeneous structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

DS-GL: Advancing Graph Learning via Harnessing the Power of Nature within Dynamic Systems

With the rapid digitization of the world, an increasing number of real-world applications are turning to nonEuclidean data, modeled as graphs. Due to their intrinsic high complexity and irregularity, learning from graph data demands tremendous computational power. Recently, CMOS-compatible Ising machines, i.e., dynamic systems composed of CMOS components, have emerged as a new approach that harnesses the inherent power of natural annealing within dynamic systems to efficiently resolve binary optimization problems and have been adopted for traditional graph computation, such as max-cut. However, when performing complex Graph Learning (GL) tasks, Ising machines face significant hurdles: (i) they are inherently binary and thus ill-suited for real-valued problems; (ii) their expensive all-to-all coupling network that guarantees effective natural annealing poses daunting scalability concerns. To address these challenges, this paper proposes a nature-powered graph learning framework dubbed DS-GL, which is the first effort to transform the process of solving graph learning problems into the natural annealing process within a parameterized dynamic system embodied as a CMOS chip. To tackle the two major hurdles, DS-GL first augments the Ising machine architecture to modify the self-reaction term of its Hamiltonian function from linear to quadratic, effectively serving as an energy regulator. This adjustment maintains the system’s original physical interpretation while enabling it to process continuous, real-valued data. Second, to address the scaling issue, DS-GL further upgrades the real-valued dense Ising machine by decomposing it into a mesh-based multi-PE dynamic system that supports efficient distributed spatial-temporal co-annealing across different PEs through sparse interconnects. By exploiting the inherent sparsity and component structures in real-world graphs, DS-GL is able to map complex graph learning tasks onto the scalable dynamic system while maintaining high accuracy. Evaluations with three diverse GL applications across six real-world datasets, including traffic flow and COVID-19 prediction, show that DS-GL can deliver from 102× to 106× speedups and 500× energy reduction over Graph Neural Networks on GPUs, with 5% - 20% accuracy enhancement.

Song, Ruibing↗

DOE OSTI2024

Efficient graph representation framework for chemical molecule similarity tasks

Graph data has emerged in numerous scientific domains and machine learning techniques have been widely used for analysis and learning of diverse data for prediction and decision. Machine learning techniques can readily address complex problems by leveraging their structural information. But graphs cannot be directly used for existing machine learning algorithms unless encoded as vectors. The problem of efficient representation of graphs is a substantial challenge in graph machine learning. In this paper, we propose a novel two-stage framework for the representation of chemical molecule graphs based on the strengths of Graph Isomorphism Networks (GINs) and Siamese autoencoders. In the first stage, the GIN model is constructed and trained using the structural information of chemical molecule graphs. Node attributes, edge attributes, and edge indices are used as input data, while graph attributes are used as labels. The GIN model effectively captures the structural characteristics of graphs and can accurately predict graph attributes, i.e., molecular properties. It also generates Graph Embeddings, represented as vectors that encode the structural information of graphs. In the second stage, Graph Embedding vectors are further optimized for downstream similarity tasks while preserving the graph structural information. The Siamese autoencoder is constructed and trained, which reduces the dimensionality of the Graph Embedding vectors, while maximizing the preservation of structural information in the original high-dimensional vectors. The resulting low-dimensional Graph Embeddings can be effectively utilized for tasks such as approximate nearest neighbor search. The experimental results demonstrate the effectiveness of our proposed framework in accurately predicting graph similarity.

Ma, Jiaji↗