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At least 253 records · Page 14

Accelerating network layouts using graph neural networks

Graph layout algorithms used in network visualization represent the first and the most widely used tool to unveil the inner structure and the behavior of complex networks. Current network visualization software relies on the force-directed layout (FDL) algorithm, whose high computational complexity makes the visualization of large real networks computationally prohibitive and traps large graphs into high energy configurations, resulting in hard-to-interpret “hairball” layouts. Here we use Graph Neural Networks (GNN) to accelerate FDL, showing that deep learning can address both limitations of FDL: it offers a 10 to 100 fold improvement in speed while also yielding layouts which are more informative. We analytically derive the speedup offered by GNN, relating it to the number of outliers in the eigenspectrum of the adjacency matrix, predicting that GNNs are particularly effective for networks with communities and local regularities. Finally, we use GNN to generate a three-dimensional layout of the Internet, and introduce additional measures to assess the layout quality and its interpretability, exploring the algorithm’s ability to separate communities and the link-length distribution. The novel use of deep neural networks can help accelerate other network-based optimization problems as well, with applications from reaction-diffusion systems to epidemics.

97 MATHEMATICS AND COMPUTING↗

Designing alloys with process-mapping AI pre-trained on empirical knowledge

<span style="font-family: Calibri, sans-serif; font-size: 12pt;">Accelerated materials design should match the recent trends in the product development cycles. Materials data analytics can be used to significantly shorten development time of specialized alloys needed for next generation energy applications. However, it faces a challenge of scarce data available for training ML models. Incorporation of the domain knowledge into deep-learning graph structure via fuzzy pre-training and causal process imitation presents a viable approach to developing accurate data-driven models and reliable alloy design tools, with limited datasets. Artificial Intelligence (AI) was used in this study to incorporate such knowledge in the domain-specific computational tool, pyroMind. The tool provides not only novel design ideas but also their interpretation via physics and engineering concepts.</span>

Romanov, Vyacheslav↗

Maximum Kolmogorov-Sinai Entropy Versus Minimum Mixing Time in Markov Chains

We establish a link between the maximization of Kolmogorov Sinai entropy (KSE) and the minimization of the mixing time for general Markov chains. Since the maximisation of KSE is analytical and easier to compute in general than mixing time, this link provides a new faster method to approximate the minimum mixing time dynamics. It could be interesting in computer sciences and statistical physics, for computations that use random walks on graphs that can be represented as Markov chains.

97 MATHEMATICS AND COMPUTING↗

Publication and Retrieval of Computational Chemical-Physical Data Via the Semantic Web. Final Technical Report

This research showed the feasibility of applying the concepts of the Semantic Web to Computation Chemistry. We have created the first web portal (www.chemsem.com) that allows data created in the calculations of quantum chemistry, and other such chemistry calculations to be placed on the web in a way that makes the data accessible to scientists in a semantic form never before possible. The semantic web nature of the portal allows data to be searched, found, and used as an advance over the usual approach of a relational database. The semantic data on our portal has the nature of a Giant Global Graph (GGG) that can be easily merged with related data and searched globally via a SPARQL Protocol and RDF Query Language (SPARQL) that makes global searches for data easier than with traditional methods. Our Semantic Web Portal requires that the data be understood by a computer and hence defined by an ontology (vocabulary). This ontology is used by the computer in understanding the data. We have created such an ontology for computational chemistry (purl.org/gc) that encapsulates a broad knowledge of the field of computational chemistry. We refer to this ontology as the Gainesville Core. While it is perhaps the first ontology for computational chemistry and is used by our portal, it is only a start of what must be a long multi-partner effort to define computational chemistry. In conjunction with the above efforts we have defined a new potential file standard (Common Standard for eXchange – CSX for computational chemistry data). This CSX file is the precursor of data in the Resource Description Framework (RDF) form that the semantic web requires. Our portal translates CSX files (as well as other computational chemistry data files) into RDF files that are part of the graph database that the semantic web employs. We propose a CSX file as a convenient way to encapsulate computational chemistry data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling Complex Relationships in Large-Scale Data using Hypergraphs (LDRD Final Report)

This SAND report documents the findings of the LDRD project, "Modeling Complex Relationships in Large-Scale Data using Hypergraphs". The project ran from October 2017 through September 2019. The focus of the project was the development and application of hypergraph data analytics to Sandia relational data applications. In this project, we attempted to apply a hypergraph data analysis method—specifically, hypergraph eigenvector centrality—to Sandia mission problems to identify influential entities (people, location, times, etc.) in the data. Unfortunately, the application data led to graph and hypergraph representations containing disconnected components. To date, there are no well-established techniques for applying eigenvector centrality to such graphs and hypergraphs. In this report, we present several heuristics for computing eigenvector centrality for disconnected graphs. We believe this is an important start to understanding how to approach the similar problem for hypergraphs, but this project concluded before we made progress on that problem. The ideas, methods, and suggestions presented here can be used for further research into this challenging problem. We also present our ideas for generating graphs with known degree and centrality distributions. The goal in presenting this work is to identify a procedure for analyzing such graphs once the problem of addressing disconnected components has been addressed. When working with a single data set, this generator can be used to create many instances of graphs that can be used to analyze the robustness of the centrality computations for the original data set. Although the results did not match perfectly in the case of the Facebook Ego dataset used in the experiments presented here, this again represents a good start in the direction of a graph generator for such problems. We note that there are potential trade-offs between how the degree and centrality distributions are fit to the original data and suggested several possible avenues for follow-on research efforts.

97 MATHEMATICS AND COMPUTING↗

HOOVER

HOOVER is a distributed framework for solving streaming/dynamic graph problems where the structure of a graph changes over time based on the state of its vertices.

97 MATHEMATICS AND COMPUTING↗

Building near-real-time processing pipelines with the spark-MPI platform

Advances in detectors and computational technologies provide new opportunities for applied research and the fundamental sciences. Concurrently, dramatic increases in the three V's (Volume, Velocity, and Variety) of experimental data and the scale of computational tasks produced the demand for new real-time processing systems at experimental facilities. Recently, this demand was addressed by the Spark-MPI approach connecting the Spark data-intensive platform with the MPI high-performance framework. In contrast with existing data management and analytics systems, Spark introduced a new middleware based on resilient distributed datasets (RDDs), which decoupled various data sources from high-level processing algorithms. The RDD middleware significantly advanced the scope of data-intensive applications, spreading from SQL queries to machine learning to graph processing. Spark-MPI further extended the Spark ecosystem with the MPI applications using the Process Management Interface. The paper explores this integrated platform within the context of online ptychographic and tomographic reconstruction pipelines.

97 MATHEMATICS AND COMPUTING↗

Fishnet four-point integrals: integrable representations and thermodynamic limits

In this work, we consider four-point integrals arising in the planar limit of the conformal “fishnet” theory in four dimensions. They define a two-parameter family of higher-loop Feynman integrals, which extend the series of ladder integrals and were argued, based on integrability and analyticity, to admit matrix-model-like integral and determinantal representations. In this paper, we prove the equivalence of all these representations using exact summation and integration techniques. We then analyze the large-order behaviour, corresponding to the thermodynamic limit of a large fishnet graph. The saddle-point equations are found to match known two-cut singular equations arising in matrix models, enabling us to obtain a concise parametric expression for the free-energy density in terms of complete elliptic integrals. Interestingly, the latter depends non-trivially on the fishnet aspect ratio and differs from a scaling formula due to Zamolodchikov for large periodic fishnets, suggesting a strong sensitivity to the boundary conditions. We also find an intriguing connection between the saddle-point equation and the equation describing the Frolov-Tseytlin spinning string in AdS 3 × S 1 , in a generalized scaling combining the thermodynamic and short-distance limits.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Synthesis and Molecular Structure of 2-(4-Chlorophenyl)-3-(phenyl-amino)-5-(thiophen-2-ylmethylidene)-3,5-dihydro-4H-imidazol-4-one

2-(4-Chlorophenyl)-3-(phenylamino)-5-(thiophen-2-ylmethylidene)-3,5-dihydro-4H-imidazol-4-one, C{sub 20}H{sub 14}N{sub 3}OSCl was synthesized and its crystal structure was determined by single crystal X-ray diffraction. The crystals are triclinic, sp. gr. P1, Z = 2. All three rings are planar, and imidazole ring is almost perpendicular to the phenyl ring with the dihedral angle of 88.65(2)°. In the crystal, pairs of O–H···O hydrogen bonds link molecules into inversion dimers, featuring R{sub 22}(10) graph set motif. Crystal structure is further stabilized by π···π interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Topology-Dependent Performance of Free-Space Photonic Quantum Networks Under Noise

Photonic quantum communication enables secure and high-fidelity information transfer beyond classical limits, with direct relevance to emerging quantum networks operating in free-space environments. While physical-layer models of depolarizing noise, Gamma–Gamma turbulence statistics, entanglement swapping, and decoy-state QKD security bounds are individually well established, prior work typically treats these components in isolation or under fixed network assumptions. In this work, we develop a unified topology-aware analytical framework that simultaneously integrates free-space optical link budgets, turbulence-induced visibility degradation, depolarizing qubit noise, multi-hop entanglement cascade dynamics, teleportation fidelity thresholds, CHSH nonlocality certification, and asymptotic decoy-state secret key rate bounds across star, mesh, and ring graph structures. Rather than introducing new physical channel models, we demonstrate that identical physical links exhibit fundamentally different end-to-end performance once embedded within different network topologies. Mesh architectures minimize visibility cascade through hop-count reduction but incur quadratic hardware scaling. Star topologies minimize link count but concentrate noise and synchronization overhead at the hub. Ring configurations offer linear hardware scaling with multiplicative fidelity degradation. The results establish topology as a first-order design parameter in near-term free-space quantum networks operating without full quantum repeater infrastructures. While motivated by distributed multi-agent architectures, the framework applies broadly to terrestrial, airborne, and satellite-assisted photonic quantum communication systems.

QKD↗

Generating Performance Models for Irregular Applications

Many applications have irregular behavior --- non-uniform input data, input-dependent solvers, irregular memory accesses, unbiased branches --- that cannot be captured using today's automated performance modeling techniques. We describe new hierarchical critical path analyses for the \Palm model generation tool. To create a model's structure, we capture tasks along representative MPI critical paths. We create a histogram of critical tasks with parameterized task arguments and instance counts. To model each task, we identify hot instruction-level sub-paths and model each sub-path based on data flow, instruction scheduling, and data locality. We describe application models that generate accurate predictions for strong scaling when varying CPU speed, cache speed, memory speed, and architecture. We present results for the Sweep3D neutron transport benchmark; Page Rank on multiple graphs; Support Vector Machine with pruning; and PFLOTRAN's reactive flow/transport solver with domain-induced load imbalance.

analytical performance models↗

GPLADD: Quantifying Trust in Government and Commercial Systems A Game-Theoretic Approach

Trust in a microelectronics-based system can be characterized as the level of confidence that a system is free of subversive alterations made during system development, or that the development process of a system has not been manipulated by a malicious adversary. Trust in systems has become an increasing concern over the past decade. This report introduces a novel game-theoretic framework, called GPLADD (Graph-based Probabilistic Learning Attacker and Dynamic Defender), for analyzing and quantifying system trustworthiness at the end of the development process, through the analysis of risk of development-time system manipulation. GPLADD represents attacks and attacker-defender contests over time. Here, time is an explicit constraint and allows incorporating the informational asymmetries between the attacker and defender into analysis. GPLADD includes an explicit representation of attack steps via multi-step attack graphs, attacker and defender strategies, and player actions at different times. GPLADD allows quantifying the attack success probability over time and the attacker and defender costs based on their capabilities and strategies. This ability to quantify different attacks provides an input for evaluation of trust in the development process. We demonstrate GPLADD on an example attack and its variants. We develop a method for representing success probability for arbitrary attacks and derive an explicit analytic characterization of success probability for a specific attack. We present a numeric Monte Carlo study of a small set of attacks, quantify attack success probabilities, attacker and defender costs, and illustrate the options the defender has for limiting the attack success and improving trust in the development process.

37 attack↗

Linear complexity

We present factorization and solution phases for a new linear complexity direct solver designed for concurrent batch operations on fine-grained parallel architectures, for matrices amenable to hierarchical representation. We focus on the strong-admissibility-based $\mathscr{H}^{2}$ format, where strong recursive skeletonization factorization compresses remote interactions. We build upon previous implementations of $\mathscr{H}^{2}$ matrix construction for efficient factorization and solution algorithm design, which are illustrated graphically in stepwise detail. The algorithms are ‘blackbox’ in the sense that the only inputs are the matrix and right-hand side, without analytical or geometrical information about the origin of the system. We demonstrate linear complexity scaling in both time and memory on four representative families of dense matrices up to one million in size. Parallel scaling up to 16 threads is enabled by a multi-level matrix graph coloring and avoidance of dynamic memory allocations thanks to prefix-sum memory management. An experimental backward error analysis is included. We break down the timings of different phases, identify phases that are memory-bandwidth limited, and discuss alternatives for phases that may be sensitive to the trend to employ lower precisions for performance.

Boukaram, Wajih↗

Enhanced Sampling of Crystal Nucleation with Graph Representation Learnt Variables

In this study, we present a graph neural network-based learning approach using an autoencoder setup to derive low-dimensional variables from features observed in experimental crystal structures. These variables are then biased in enhanced sampling to observe state-to-state transitions and reliable thermodynamic weights. Our approach uses simple convolution and pooling methods. To verify the effectiveness of our protocol, we examined the nucleation of various allotropes and polymorphs of iron and glycine from their molten states. Our graph latent variables when biased in well-tempered metadynamics consistently show transitions between states and achieve accurate free energy calculations in agreement with experiments, both of which are indicators of dependable sampling. This underscores the strength and promise of our graph neural net variables for improved sampling. Furthermore, the protocol shown here should be applicable for other systems and with other sampling methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Continuous integration data-driven platform of industrial-scale subsurface storage for real-time analytics

This project helped address the growing need for efficient and scalable models to support geological carbon and energy storage, which are crucial for achieving net-zero emissions. Traditionally accurate high-fidelity numerical models have been used to simulate relevant storage processes under a handful of processes, however such models are computationally demanding, making uncertainty quantification impractical. Consequently, we first developed a machine learning framework, based on Graph Neural Operators (GNOs), to improving the accuracy of model predictions for a fixed computational budget. We then developed an Ensemble of Improved Neural Operators (ENO), which uses bagging and Monte Carlo dropout techniques, to further improve prediction accuracy. Lastly, we developed the way to explain progressive transfer learning methods to reduce the amount of training data and computational cost of training (i.e., reduce trainable parameters) when using our models for multiple storage sites. Our numerical investigation, which used real-world case studies, demonstrated that our framework can significantly improve the safety and efficiency of geological storage operations, with potential applications in other domains such as geothermal reservoirs and climate modeling.

54 ENVIRONMENTAL SCIENCES↗

Locality-aware and load-balanced static task scheduling for MapReduce

Task scheduling for MapReduce jobs has been an active area of research with the objective of decreasing the amount of data transferred during the shuffle phase via exploiting data locality. In the literature, generally only the scheduling of reduce tasks is considered with the assumption that scheduling of map tasks is already determined by the input data placement. However, in cloud or HPC deployments of MapReduce, the input data is located in a remote storage and scheduling map tasks gains importance. Here, we propose models for simultaneous scheduling of map and reduce tasks in order to improve data locality and balance the processors’ loads in both map and reduce phases. Our approach is based on graph and hypergraph models which correctly encode the interactions between map and reduce tasks. Partitions produced by these models are decoded to schedule map and reduce tasks. A two-constraint formulation utilized in these models enables balancing processors’ loads in both map and reduce phases. The partitioning objective in the hypergraph models correctly encapsulates the minimization of data transfer when a local combine step is performed prior to shuffle, whereas the partitioning objective in the graph models achieve the same feat when a local combine is not performed. Here, we show the validity of our scheduling on the MapReduce parallelizations of two important kernel operations – sparse matrix–vector multiplication (SpMV) and generalized sparse matrix–matrix multiplication (SpGEMM) – that are widely encountered in big data analytics and scientific computations. Compared to random scheduling, our models lead to tremendous savings in data transfer by reducing data traffic from several hundreds of megabytes to just a few megabytes in the shuffle phase and consequently leading up to 2.6x and 4.2x speedup for SpMV and SpGEMM, respectively.

97 MATHEMATICS AND COMPUTING↗

Energy landscapes for a machine learning application to series data

Methods developed to explore and characterise potential energy landscapes are applied to the corresponding landscapes obtained from optimisation of a cost function in machine learning. We consider neural network predictions for the outcome of local geometry optimisation in a triatomic cluster, where four distinct local minima exist. The accuracy of the predictions is compared for fits using data from single and multiple points in the series of atomic configurations resulting from local geometry optimisation and for alternative neural networks. The machine learning solution landscapes are visualised using disconnectivity graphs, and signatures in the effective heat capacity are analysed in terms of distributions of local minima and their properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗