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EXAGRAPH: Graph and combinatorial methods for enabling exascale applications

Combinatorial algorithms in general and graph algorithms in particular play a critical enabling role in numerous scientific applications. However, the irregular memory access nature of these algorithms makes them one of the hardest algorithmic kernels to implement on parallel systems. With tens of billions of hardware threads and deep memory hierarchies, the exascale computing systems in particular pose extreme challenges in scaling graph algorithms. The codesign center on combinatorial algorithms, ExaGraph, was established to design and develop methods and techniques for efficient implementation of key combinatorial (graph) algorithms chosen from a diverse set of exascale applications. Algebraic and combinatorial methods have a complementary role in the advancement of computational science and engineering, including playing an enabling role on each other. In this paper, we survey the algorithmic and software development activities performed under the auspices of ExaGraph from both a combinatorial and an algebraic perspective. In particular, we detail our recent efforts in porting the algorithms to manycore accelerator (GPU) architectures. We also provide a brief survey of the applications that have benefited from the scalable implementations of different combinatorial algorithms to enable scientific discovery at scale. We believe that several applications will benefit from the algorithmic and software tools developed by the ExaGraph team.

97 MATHEMATICS AND COMPUTING↗

Graph neural networks for detecting anomalies in scientific workflows

Identifying and addressing anomalies in complex, distributed systems can be challenging for reliable execution of scientific workflows. We model these workflows as directed acyclic graphs (DAGs), where the nodes and edges of the DAGs represent jobs and their dependencies, respectively. We develop graph neural networks (GNNs) to learn patterns in the DAGs and to detect anomalies at the node (job) and graph (workflow) levels. We investigate workflow-specific GNN models that are trained on a particular workflow and workflow-agnostic GNN models that are trained across the workflows. Our GNN models, which incorporate both individual job features and topological information from the workflow, show improved accuracy and efficiency compared to conventional learning methods for detecting anomalies. While joint trained with multiple scientific workflows, our GNN models reached an accuracy more than 80% for workflow level and 75% for job level anomalies. In addition, we illustrate the importance of hyperparameter tuning method in our study that can significantly improve the metric(s) measure of evaluating the GNN models. Finally, we integrate explainable GNN methods to provide insights on job features in the workflow that cause an anomaly.

97 MATHEMATICS AND COMPUTING↗

HydraGNN_Predictive_GFM_2026 - Ensemble of predictive graph foundation models for atomistic materials modeling

This release contains data and parameters of HydraGNN-based graph foundation models trained as a result of the work published in the pre-print "Exascale Multi-Task Graph Foundation Models for Imbalanced, Multi-Fidelity Atomistic Data" by M. Lupo Pasini et al. (https://arxiv.org/abs/2604.15380). We jointly train on 16 open first-principles datasets (544+ million structures covering 85+ elements) using a multi-task architecture with per-dataset heads and a scalable ADIOS2/DDStore data pipeline. On Frontier, we execute six large-scale DeepHyper hyperparameter optimization campaigns in FP64 and promote the top-performing message-passing models to sustained 2,048-node training, yielding a PaiNN-based lead model. The version of HydraGNN used to generate the outputs provided in this release is HydraGNN v5.0 (https://github.com/ORNL/HydraGNN/releases/tag/v5.0) The list of datasets used for the training of the graph foundation model is the following: 1) Alexandria [1] 2) ANI1x [2] 3) MPTrj [3] 4) Open Catalyst 2020 (OC20) [4] 5) Open Catalyst 2022 (OC22) [5] 6) Open Catalyst 2025 (OC25) [6] 7) Open Direct ir Capture 2023 (ODAC23) [7] 8) Open Materials 2024 (OMat24) [8] 9) Open Molecules 2025 (OMol25) [9] 10) OMol25-neutral (subset of OMol25 that contains only molecules with zero total charge) 11) OMol25-non-neutral (subset of OMol25 that contains only molecules with non-zero total charge) 12) Open Polymers 2026 (OPoly2026) [10] 13) Nabla2DFT [11] 14) QCML [12] 15) QM7X [reference 13] 16) transition1x [14] Dataset references: [1] J. Schmidt et al., “A dataset of 175k stable and metastable materials calculated with the PBEsol and SCAN functionals,” Scientific Data, vol. 9, p. 64, 2022. [2] J. S. Smith et al., “The ANI-1ccx and ANI-1x data sets, coupled-cluster and density functional theory properties for molecules,” Scientific Data, vol. 7, p. 134, 2020. [Online]. Available: https: //www.nature.com/articles/s41597-020-0473-z [3] A. Jain et al., “Commentary: The Materials Project: A materials genome approach to accelerating materials innovation,” APL Materials, vol. 1, no. 1, p. 011002, 07 2013. [Online]. Available: https://doi.org/10.1063/1.4812323 [4] L. Chanussot et al., “Open catalyst 2020 (oc20) dataset and community challenges,” ACS Catalysis, vol. 11, no. 10, pp. 6059–6072, 2021. [Online]. Available: https://doi.org/10.1021/acscatal.0c04525 [5] K. Tran et al., “Open catalyst 2022 (oc22) dataset and challenges for oxidation electrocatalysts,” ACS Catalysis, vol. 13, no. 5, pp. 3066–3084, 2023. [Online]. Available: https://doi.org/10.1021/acscatal.2c05426 [6] S. J. Sahoo et al., “The open catalyst 2025 (oc25) dataset and models for solid-liquid interfaces,” arXiv preprint arXiv:2509.17862, 2025. [Online]. Available: https://arxiv.org/abs/2509.17862 [7] A. Sriram et al., “The open DAC 2023 dataset and challenges for sorbent discovery in direct air capture,” ACS Central Science, vol. 10, no. 5, pp. 923–941, 2024. [8] L. Barroso-Luque et al., “Open materials 2024 (omat24) inorganic materials dataset and models,” 2024. [Online]. Available: https://arxiv.org/abs/2410.12771 [9] D. S. Levine et al., “The open molecules 2025 (OMol25) dataset, evaluations, and models,” 2025. [Online]. Available: https://arxiv.org/abs/2505.08762 [10] D. S. Levine et al., The open polymers 2026 (OPoly26) dataset and evaluations,” arXiv preprint arXiv:2512.23117, 2025. [Online]. Available: https://arxiv.org/abs/2512.23117 [11] K. Khrabrov et al., “Nabla2dft: A universal quantum chemistry dataset of drug-like molecules and a benchmark for neural network potentials,” in NeurIPS 2024 Datasets and Benchmarks Track, 2024. [Online]. Available: https://openreview.net/forum?id=ElUrNM9U8c [12] S. Ganscha et al., “The QCML dataset, quantum chemistry reference data from 33.5M DFT and 14.7B semi-empirical calculations,” Scientific Data, vol. 12, p. 406, 2025. [13] J. Hoja et al., “QM7-X, a comprehensive dataset of quantum-mechanical properties spanning the chemical space of small organic molecules,” Scientific Data, vol. 8, p. 43, 2021. [Online]. Available: https://www.nature.com/articles/s41597-021-00812-2 [14] M. Schreiner et al., “Transition1x - a dataset for building generalizable reactive machine learning potentials,” Scientific Data, vol. 9, p. 779, 2022. The folder "datasets_ADIOS2_format" contains the set of pre-processed datasets in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used for the development and training of GFMs in this work. The "datasets_ADIOS2_format" directory contains 2 sub-directories, one for the version "v1" of the datasets and one for the version "v2" of the datasets. The version "v1" of the datasets provides values of the total energy as they are extracted from the original data as it was released by the respective institutions. The version "v2" of the datasets provides values of the energy that have been realigned. The realignment was performed by training a linear regression model that predicts the total energy as a function of the chemical composition of the atomistic structure, and then subtract such prediction from the original value of the total energy. Both folders "v1" and "v2" contain 16 sub-directories, each corresponding to an ADIOS2-formatted dataset The folder "DeepHyper-results" contains the configurational files and model's parameters for all the 186 HPO trials that were successfully completed by the scalable hyperparameter optimization (HPO) runs on Frontier. The content of the folder "DeepHyper-results" I structured as follows: 1) task-list.txt: list of mpnn name, jobid, and deephyper task id 2) gfm_${MPNN}_${JOBID}_0.${TASKID}: run directory with checkpoint files 3) gfm_${MPNN}: deephyper summary directory (*.csv) for each specific MPNN type 4) deephyper-experiment-${JOBID}: output and error logs for each job The file "deephyper-sorted.csv" contains the details of each HydraGNN model built and tested by HPO, obtained by merging the (*.csv) filed from each HPO run executed. Out of all the HPO trials, we selected 10 to continue the training of the respective HydraGNN models. Due to limited computational budget available in the LRN070 allocation we could not complete the training till convergence for all these 10 selected models. The folder "models" contains multiple sub-folders, one per each HydraGNN model trained. Each model sub-folder contains the parameters of each HydraGNN model, with multiple checkpoint-restarts. The list of sub-folders are as follows: 1) multidataset_hpo-BEST1-fp64 2) multidataset_hpo-BEST2-fp64 3) multidataset_hpo-BEST3-fp64 4) multidataset_hpo-BEST4-fp64 5) multidataset_hpo-BEST5-fp64 6) multidataset_hpo-BEST6-fp64 7) multidataset_hpo-BEST7-fp64 8) multidataset_hpo-BEST8-fp64 9) multidataset_hpo-BEST9-fp64 10) multidataset_hpo-BEST10-fp64 Within each one of these folders, additional auxiliary log files are provided with descriptions about how the training proceeded. The lead PaiNN-model is contained inside "multidataset_hpo-BEST6-fp64". The file "mlp_branch_weights" contains the parameters of the multi-layer perceptron (MLP) used to reconcile the predictions of the 16 output decoding heads of the HydragNN architectures. The MLP takes in input the chemical composition of the atomistic structure and predicts averaging weights to linearly mix the predictions of each output decoding head toward consolidating them into a single one. The folder "1.1billion-structure-inference" contains 1.1 billion atomistic structures randomly generated. Each structures is associated with energy and forces predicted with the lead-PaiNN model combined with the MLP model for reconciliation of the multi-branch predictions generated by the 16 output decoding heads. The folder "1.1billion-structure-inference" contains 9,300 (*.tar.gz) subdirectories, one per Frontier compute node used to execute the inference at exascale. Once uncompressed, each (*.tar.gz) subdirectory contains an ADIOS2 (*.bp) file container, where each atomistic structure is stored as a PyTorch-Geometric Data object. The file "export_dataset_environment_variables.sh" contains the environment variables that need to be set before running the HydraGNN code to reproduce the results provided in this dataset release. The code that can be used to load the ADIOS2 files, load HydraGNN models, and run inference is available at: https://github.com/ORNL/HydraGNN/releases/tag/v5.0

36 MATERIALS SCIENCE↗

Distance-Weighted Graph Neural Networks on FPGAs for Real-Time Particle Reconstruction in High Energy Physics

Graph neural networks have been shown to achieve excellent performance for several crucial tasks in particle physics, such as charged particle tracking, jet tagging, and clustering. An important domain for the application of these networks is the FGPA-based first layer of real-time data filtering at the CERN Large Hadron Collider, which has strict latency and resource constraints. We discuss how to design distance-weighted graph networks that can be executed with a latency of less than one μs on an FPGA. To do so, we consider a representative task associated to particle reconstruction and identification in a next-generation calorimeter operating at a particle collider. We use a graph network architecture developed for such purposes, and apply additional simplifications to match the computing constraints of Level-1 trigger systems, including weight quantization. Using the hls4ml library, we convert the compressed models into firmware to be implemented on an FPGA. Performance of the synthesized models is presented both in terms of inference accuracy and resource usage.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Directed Acyclic Graph Guidance Documentation

For over a decade, the National Aeronautics and Space Administration (NASA) has tracked and configuration-managed approximately 30 risks to astronaut health and performance that occur before, during and after spaceflight. The Human System Risk Board (HSRB), a Health and Medical Technical Authority (HMTA) Board at NASA Johnson Space Center, is the entity responsible for identifying, assessing, analyzing, and monitoring the official understanding of the risk or risk posture for each of the Human System Risks and determining – based on evaluation of the available evidence – when that risk posture changes. The ultimate purpose of tracking and researching these risks is to find ways to reduce the risk that astronaut crews face during spaceflight. Historically, research, development and operations relevant to one risk have been conducted in isolation from other risks; these individual risk ‘silos’ enabled initial characterization of each specific risk. In spaceflight however, the impact of exposure to risk for astronaut crews is cumulative, and not independent of exposures or other risks, as all the adverse effects of the spaceflight environment begin at launch, continue throughout the duration of the mission and in some cases across the lifetime of the crews. In January of 2020, the HSRB at NASA embarked on a pilot project designed to assess the potential value of causal diagramming as a tool to facilitate understanding these cumulative and interdependent effects as applied within Human System Risk management. This process uses directed acyclic graphs as a means of formalizing a shared mental model of the causal flow of risk among Risk Board stakeholders. Initially this model was to improve communication among those stakeholders, but the potential value exceeds communication alone. Formalization of the process for creating these causal diagrams will enable the creation of a composite risk network that is vetted by members of the NASA community and configuration managed. The causal diagrams are formulated as directed acyclic graphs (DAGs) to function as a type of knowledge graph for reference for the board and its stakeholders. This document outlines the pilot process, the standardized approaches, and guidance for risk custodian teams when creating and updating DAGs as a part of the NASA Human System Risk Management process.

Risk↗

Multigraph-based Routing in Delay Tolerant Networks: An Alternative to Contact Graph Routing

Satellites are leaving the realms of niche use, extending our day-to-day networked infrastructure to space – thereby forcing a generalization of network architectures. The Delay Tolerant Networking (DTN) protocol is being developed to give rise to this new Solar System Internet. Predominantly, DTNs in space use globally-distributed contact tables to compute routes. In this paper, we propose and analyze a novel optimized approach for route computations that improves upon traditional approaches. As the general DTN will always include some scheduled links, our new algorithm enables greater scalability and practicality of DTN routing. These contact tables include windows when two nodes can communicate and were classically organized into a contact graph, where the vertices represent contact opportunities. Because the complexity of a contact graph grows with the number of contacts, pathfinding on it does not scale. A new structure using multigraphs with the same data is proposed. We show that a multigraph-based approach, which we call contact multigraph routing, exhibits performance superior to routing based on contact graphs, allowing greater scaling to schedule-based routing. In this paper, the multigraph-based algorithm is detailed and a proof is included showing it outperforms the previous algorithm given the same input. Pseudocode is included, as are simulation results. We conclude with suggested future work.

Delay Tolerant Networking↗

Requirement Discovery Using Embedded Knowledge Graph With ChatGPT

The field of Advanced Air Mobility (AAM) is witnessing a transformation with innovations such as electric aircraft and increasingly automated airspace operations. Within AAM, the Urban Air Mobility (UAM) con-cept focuses on providing air-taxi services in densely populated urban areas. This research introduces the utilization of Large Language Models (LLMs), such as OpenAI's GPT-4, to enhance the UAM Requirement discovery process. This study explores two distinct approaches to leverage LLMs in the context of UAM Requirement discovery. The first approach evaluates the LLM's ability to provide responses without relying on additional outside systems, such as a relational or graph database. Instead, a vector store provides relevant information to the LLM based on the user’s question, a process known as Retrieval Augmented Generation (RAG). The second approach integrates the LLM with a graph database. The LLM acts as an intermediary between the user and the graph database, translating user questions into cypher queries for the database and database responses into human-readable answers for the user. Our team implemented and tested both solutions to analyze require-ments within a UAM dataset. This paper will talk about our approaches, implementations, and findings related to both approaches.

systems engineering↗

Requirement Discovery Using Embedded Knowledge Graph with ChatGPT

The field of Advanced Air Mobility (AAM) is witnessing a transformation with innovations such as electric aircraft and increasingly automated airspace operations. Within AAM, the Urban Air Mobility (UAM) concept focuses on providing air-taxi services in densely populated urban areas. This research introduces the utilization of Large Language Models (LLMs), such as OpenAI's GPT-4, to enhance the UAM Requirement discovery process. This study explores two distinct approaches to leverage LLMs in the context of UAM Requirement discovery. The first approach evaluates the LLM's ability to provide responses without relying on additional outside systems, such as a relational or graph database. Instead, a vector store provides relevant information to the LLM based on the user’s question, a process known as Retrieval Augmented Generation (RAG). The second approach integrates the LLM with a graph database. The LLM acts as an intermediary between the user and the graph database, translating user questions into cypher queries for the database and database responses into human-readable answers for the user. Our team implemented and tested both solutions to analyze requirements within a UAM dataset. This paper will talk about our approaches, implementations, and findings related to both approaches.

systems engineering↗

Requirement Discovery Using Embedded Knowledge Graph With ChatGPT - Poster

The field of Advanced Air Mobility (AAM) is witnessing a transformation with innovations such as electric aircraft and increasingly automated airspace operations. Within AAM, the Urban Air Mobility (UAM) con-cept focuses on providing air-taxi services in densely populated urban areas. This research introduces the utilization of Large Language Models (LLMs), such as OpenAI's GPT-4, to enhance the UAM Requirement discovery process. This study explores two distinct approaches to leverage LLMs in the context of UAM Requirement discovery. The first approach evaluates the LLM's ability to provide responses without relying on additional outside systems, such as a relational or graph database. Instead, a vector store provides relevant information to the LLM based on the user’s question, a process known as Retrieval Augmented Generation (RAG). The second approach integrates the LLM with a graph database. The LLM acts as an intermediary between the user and the graph database, translating user questions into cypher queries for the database and database responses into human-readable answers for the user. Our team implemented and tested both solutions to analyze require-ments within a UAM dataset. This paper will talk about our approaches, implementations, and findings related to both approaches.

systems engineering↗

Airspace Research and Development Portfolio Assessment of Urban Air Mobility using Knowledge Graph Data Science

National Aeronautics and Space Administration (NASA) is spearheading an innovative digital engineering approach to integrate, communicate, and facilitate the research of Urban Air Mobility (UAM) operations. The UAM vision is one in which advanced technologies and new operational procedures enable practical and cost-effective air transport as an integrated mode of movement of people and goods throughout metropolitan areas. To safely support UAM operations at scale in the National Airspace System (NAS), NASA’s Air Traffic Management-Exploration (ATM-X) project has been conducting research that evolves the UAM air traffic management system towards a highly automated and operationally flexible system of the future. The complexity of UAM airspace evolution to accommodate the increasing tempo of UAM operations over time is managed through the UAM airspace research roadmap, which is a system engineering approach to the R&D of complex system-of-systems, where system’s interdependencies make it nearly impossible to define requirements for individual elements of the system in isolation. These interdependencies form a knowledge graph (node-link network) with a highly complex structure far beyond the human user’s ability to extract insights for project management’s research portfolio assessment. This study applies advanced data analytics in knowledge graph to the UAM knowledge graph to facilitate the portfolio assessment.

ATM↗

Airspace Research and Development Portfolio Assessment of Urban Air Mobility using Knowledge Graph Data Science

National Aeronautics and Space Administration (NASA) is spearheading an innovative digital engineering approach to integrate, communicate, and facilitate the research of Urban Air Mobility (UAM) operations. The UAM vision is one in which advanced technologies and new operational procedures enable practical and cost-effective air transport as an integrated mode of movement of people and goods throughout metropolitan areas. To safely support UAM operations at scale in the National Airspace System (NAS), NASA’s Air Traffic Management-Exploration (ATM-X) project has been conducting research that evolves the UAM air traffic management system towards a highly automated and operationally flexible system of the future. The complexity of UAM airspace evolution to accommodate the increasing tempo of UAM operations over time is managed through the UAM airspace research roadmap, which is a system engineering approach to the R&D of complex system-of-systems, where system’s interdependencies make it nearly impossible to define requirements for individual elements of the system in isolation. These interdependencies form a knowledge graph (node-link network) with a highly complex structure far beyond the human user’s ability to extract insights for project management’s research portfolio assessment. This study applies advanced data analytics in knowledge graph to the UAM knowledge graph to facilitate the portfolio assessment.

ATM↗

Graph Representation Learning for Dengue Forecasting

In 2017, the largest recorded dengue outbreak in Sri Lanka’s history occurred. Since then, dengue has continued to threaten national health across Sri Lanka. The development of an effective Early Warning System (EWS) for dengue outbreaks is essential for Sri Lanka’s Ministry of Health to take preventative measures. We propose the use of Graph Neural Networks as EWS. Using earth observational data from NASAs global satellites and dengue incidence data from Sri Lanka s Ministry of Health, we developed a series of traditional and graph representation EWS to forecast Dengue cases across Sri Lanka’s 25 districts between 2013 and 2022. We demonstrate empirically that Graph Neural Networks which incorporate spatiotemporal relations significantly outperform traditional EWS such as Autoregressive Integrated Moving Average (ARIMA), Random Forest, and Long Short-Term Memory (LSTM). Our source code is available on GitHub and will be provided in the final submission.

Graph Neural Networks↗

A Knowledge Graph Framework for Organizing Heterogeneous Datasets for Utilization in Classical and Quantum Computing: Current Challenges and Future Directions

"The escalating impact of climate change induced extreme weather events in urban, suburban, and rural environments demands a rethink of how we have been using the single event-based or use-case-based knowledge graph models. The lack of representation in interaction within environmental variables found in literature led to the development of a novel framework that reflects the true nature of the interconnectedness in our environment. We propose an Environmental Interaction Knowledge Graph (EIKG) framework. This general EIKG framework works as the basis for interconnected environmental events by knitting interrelated events such as hurricanes leading to storm surges, which lead to flood events that could cause mudslides, landslides, etc., The cascading nature of one event leading to another related event in the environment requires an adequate understanding of each event using contextual information before conducting any data-driven analytics. This vision paper showcases how the EIKG:floods, EIKG:wildfire EIKG:landslides, etc, can be derived from a base case framework of EIKG as those individual events are interconnected with some common denominator variables. As an example, the precipitation variable is used in the flood case study as well as in the wildfire case study, as excessive precipitation levels lead to floods, and lack of precipitation leads to droughts and wildfires. We identify the precipitation variable as a “common-denominator-variable” in extreme weather events that play a key role in modeling the environment leading to different extreme weather events based on the variability of that variable (varying values where low precipitation leads to drought, and high values lead to floods). We use the insights gained from EIKG to conduct classical and Quantum Machine Learning (QML) based data analysis on the research questions developed. Our preliminary study shows how the Variational Quantum Classifier (VQC) and Quantum Support Vector Classifier (QSVC) are used along with the classical machine learning models to compare the model accuracies. Our study elaborates on how a quantitative analysis uses state-of-the-art machine learning techniques that include implementing both classical and quantum machine learning models and developing the knowledge graph. The EIKG is used to organize heterogeneous datasets and integrate the relations to case-specific extreme weather events such as floods. The study uses datasets such as county-to-country residential mobility data, socioeconomic datasets from the US Census Bureau, climate and weather-related Earth Observational data from NASA, and critical infrastructure data from the Homeland Infrastructure datasets."

Knowledge Graphs, Quantum Computing, Heterogenous ↗

Development of message passing-based graph convolutional networks for classifying cancer pathology reports

Abstract Background Applying graph convolutional networks (GCN) to the classification of free-form natural language texts leveraged by graph-of-words features (TextGCN) was studied and confirmed to be an effective means of describing complex natural language texts. However, the text classification models based on the TextGCN possess weaknesses in terms of memory consumption and model dissemination and distribution. In this paper, we present a fast message passing network (FastMPN), implementing a GCN with message passing architecture that provides versatility and flexibility by allowing trainable node embedding and edge weights, helping the GCN model find the better solution. We applied the FastMPN model to the task of clinical information extraction from cancer pathology reports, extracting the following six properties: main site, subsite, laterality, histology, behavior, and grade. Results We evaluated the clinical task performance of the FastMPN models in terms of micro- and macro-averaged F1 scores. A comparison was performed with the multi-task convolutional neural network (MT-CNN) model. Results show that the FastMPN model is equivalent to or better than the MT-CNN. Conclusions Our implementation revealed that our FastMPN model, which is based on the PyTorch platform, can train a large corpus (667,290 training samples) with 202,373 unique words in less than 3 minutes per epoch using one NVIDIA V100 hardware accelerator. Our experiments demonstrated that using this implementation, the clinical task performance scores of information extraction related to tumors from cancer pathology reports were highly competitive.

59 BASIC BIOLOGICAL SCIENCES↗

Testing CP properties of the Higgs boson coupling to τ leptons with heterogeneous graphs

In this paper we explore the possibility of utilizing Deep Learning in measuring the CP properties of the coupling of Higgs boson to τ leptons at the High Luminosity Large Hadron Collider. We employ three Deep Learning (DL) networks, Multi-Layer Perceptron (MLP), Graph Convolution Network (GCN), and Graph Transformer Network (GTN) to enhance signal-to-background separation. The angle between τ lepton decay planes at the detector level is CP-sensitive observables, and we develop Heterogeneous Graphs that integrate diverse node and edge structures to incorporate the CP-sensitive observable efficiently. Using simplified detector simulations we estimate the reconstruction accuracy of the angle between τ lepton planes at the detector level, considering hadronic τ decay modes and standard model backgrounds. With $\sqrt{s}$ = 14 TeV and $\mathcal{L}$ = 100 fb -1 , MLP excludes CP mixing angles above 20° at 68% confidence level (CL), while GCN and GTN achieve exclusions at 90% CL and 95% CL, respectively. The networks also achieve a 3σ significance in excluding a pure CP-odd state.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Symbol alphabets from plabic graphs

Symbol alphabets of n-particle amplitudes in N = 4 super-Yang-Mills theory are known to contain certain cluster variables of Gr(4, n) as well as certain algebraic functions of cluster variables. In this paper we suggest an algorithm for computing these symbol alphabets from plabic graphs by solving matrix equations of the form C ∙ Z = 0 to associate functions on Gr(m, n) to parameterizations of certain cells of Gr(k, n) indexed by plabic graphs. For m = 4 and n = 8 we show that this association precisely reproduces the 18 algebraic symbol letters of the two-loop NMHV eight-particle amplitude from four plabic graphs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Gauge loop-string-hadron formulation on general graphs and applications to fully gauge fixed Hamiltonian lattice gauge theory

We develop a gauge invariant, Loop-String-Hadron (LSH) based representation of SU(2) Yang-Mills theory defined on a general graph consisting of vertices and half-links. Inspired by weak coupling studies, we apply this technique to maximal tree gauge fixing. This allows us to develop a fully gauge-fixed representation of the theory in terms of LSH quantum numbers. We explicitly show how the quantum numbers in this formulation directly relate to the variables in the magnetic description. In doing so, we will also explain in detail how the Kogut-Susskind formulation, prepotentials, and point splitting work for general graphs. In the appendix of this work, we provide a self-contained exposition of the mathematical details of Hamiltonian pure gauge theories defined on general graphs.

Algorithms and Theoretical Developments↗

Efficient estimation of the modified Gromov–Hausdorff distance between unweighted graphs

Abstract Gromov–Hausdorff distances measure shape difference between the objects representable as compact metric spaces, e.g. point clouds, manifolds, or graphs. Computing any Gromov–Hausdorff distance is equivalent to solving an NP-hard optimization problem, deeming the notion impractical for applications. In this paper we propose a polynomial algorithm for estimating the so-called modified Gromov–Hausdorff (mGH) distance, a relaxation of the standard Gromov–Hausdorff (GH) distance with similar topological properties. We implement the algorithm for the case of compact metric spaces induced by unweighted graphs as part of Python library , and demonstrate its performance on real-world and synthetic networks. The algorithm finds the mGH distances exactly on most graphs with the scale-free property. We use the computed mGH distances to successfully detect outliers in real-world social and computer networks.

Oles, Vladyslav (ORCID:0000000188727463)↗