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A computation graph is accessed. In the computation graph, operations to be performed are represented as interior nodes, inputs to the operations are represented as leaf nodes, and a result of the operations is represented as a root. Selected sets of the operations are combined to form respective kernels of operations. Code is generated execute the kernels of operations. The code is executed to determine the result.
Global supply chains for critical minerals and materials are complex, evolving networks of countries, products, production stages, and trade relationships. Existing analytical approaches are limited by fragmented data and static network representations that do not capture the dynamic production dependencies linking raw materials, intermediate products, and final goods across multiple countries. Trade and production statistics provide only a partial view of domestic production, inventories, and material flows, making it difficult to identify indirect sourcing pathways, hidden dependencies, and embedded foreign exposures. This paper introduces the Supply Chain Exposure Network Tracking and Risk Assessment (SENTRA) framework, a modular graph-based computational framework for constructing, analyzing, and forecasting dynamic supply chain networks. As the first paper in a three-part methodological series, it establishes the computational foundation of SENTRA by constructing a temporal attributed multi-relational graph whose nodes represent product–country pairs and whose edges encode observed trade and within-country value-chain relationships. Statistical estimation and constrained optimization recover latent production, final demand, and product input dependency coefficients while enforcing economic accounting constraints. Graph-derived exposure measures quantify direct, transshipment, value-chain, and multi-hop supply chain dependencies independently of the forecasting model. A temporal graph forecasting architecture based on a relational graph neural network then forecasts the evolution of the graph under mass-balance constraints with distribution-free conformal uncertainty quantification. Validation on the global aluminum supply chain shows that the learned graph representations recover economically meaningful supply chain structure, accurately forecast out-of-sample trade relationships, and produce well-calibrated prediction intervals. Subsequent papers apply this computational foundation to exposure assessment, disruption analysis, and scenario-based policy analysis, and extend the framework to multimaterial supply chain modeling and decision support.
This paper presents a new method for enhancing Alternating Current Power Flow (ACPF) analysis. The method integrates the Newton-Raphson (NR) method with Enhanced-Gradient Descent (GD) and computational graphs. The integration of renewable energy sources in power systems introduces variability and unpredictability, and this method addresses these challenges. It leverages the robustness of NR for accurate approximations and the flexibility of GD for handling variable conditions, all without requiring Jacobian matrix inversion. Furthermore, computational graphs provide a structured and visual framework that simplifies and systematizes the application of these methods. The goal of this fusion is to overcome the limitations of traditional ACPF methods and improve the resilience, adaptability, and efficiency of modern power grid analyses. We validate the effectiveness of our advanced algorithm through comprehensive testing on established IEEE benchmark systems. Furthermore, our findings demonstrate that our approach not only speeds up the convergence process but also ensures consistent performance across diverse system states, representing a significant advancement in power flow computation.
The reconstruction of charged particle trajectories at the Large Hadron Collider and future colliders relies on energy depositions in sensors placed at distances ranging from a centimeter to a meter from the colliding beams. We propose a method of detecting charged particles that decay invisibly after traversing a short distance of about 25 cm inside the experimental apparatus. One of the decay products may constitute the dark matter known to be 84% of all matter at galactic and cosmological distance scales. Our method uses graph computing to cluster spacepoints recorded by two-dimensional silicon pixel sensors into mathematically-defined patterns. The algorithm may be implemented on silicon-based integrated circuits using field-programmable gate array technology to augment or replace traditional computing platforms.
Abstract Image recognition is a pervasive task in many information-processing environments. We present a solution to a difficult pattern recognition problem that lies at the heart of experimental particle physics. Future experiments with very high-intensity beams will produce a spray of thousands of particles in each beam-target or beam-beam collision. Recognizing the trajectories of these particles as they traverse layers of electronic sensors is a massive image recognition task that has never been accomplished in real time. We present a real-time processing solution that is implemented in a commercial field-programmable gate array using high-level synthesis. It is an unsupervised learning algorithm that uses techniques of graph computing. A prime application is the low-latency analysis of dark-matter signatures involving metastable charged particles that manifest as disappearing tracks.
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Computationally complex primitive operations of an algorithm are executed concurrently in a plurality of functional units under the control of an assignment manager. The algorithm is preferably defined as a computationally marked graph contianing data status edges (paths) corresponding to each of the data flow edges. The assignment manager assigns primitive operations to the functional units and monitors completion of the primitive operations to determine data availability using the computational marked graph of the algorithm. All data accessing of the primitive operations is performed by the functional units independently of the assignment manager.
The project that developed this is unclassified, with the mandate to produce open source code. This code computes the hitting time moments of a graph using a linear algebra configuration. The goal of this work is to explore the performance capabilities of the Chapel programming language. Toward that end, we generate random adjacency matrices which represent a random graph. The code can also read in an adjacency matrix from a file. The main computation is the Conjugate Gradient method.SAND2020-12651 M. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
This paper presents an open-source, parallel AI environment (named OpenGraphGym) to facilitate the application of reinforcement learning (RL) algorithms to address combinatorial graph optimization problems. This environment incorporates a basic deep reinforcement learning method, and several graph embeddings to capture graph features, it also allows users to rapidly plug in and test new RL algorithms and graph embeddings for graph optimization problems. This new open-source RL framework is targeted at achieving both high performance and high quality of the computed graph solutions. This RL framework forms the foundation of several ongoing research directions, including 1) benchmark works on different RL algorithms and embedding methods for classic graph problems; 2) advanced parallel strategies for extreme-scale graph computations, as well as 3) performance evaluation on real-world graph solutions.
An important class of data analysis tasks stem from comparing subsets of connected records within massive sets of complex relational data. A common approach is to represent each set of connected records with a small graph, or set of data entities (graph vertices) and their relationships (graph edges), and efficient methods to gauge similarity for pairs of graphs are of high interest. This project concentrated on dynamic graphs, where each edge record has an associated timestamp denoting the time of observation. Pre-existing techniques for comparing dynamic graphs concentrate on either computing graph edit distance (number of vertex and edge deletion, addition, and timestamp modifications) or vectorizing the graph with counts of a limited set of dynamic graph motifs (tiny fundamental subgraphs) and computing distances between the vectors. These approaches are less able to see similarities in graphs that are fairly different in size but come from identical graph generation processes. The motif counting approach can be improved for graphs from the same process, but suffers from requiring many types of motifs meaning it is expensive. Moreover, many motifs are not present for small graphs, meaning realizing a a much larger graph came from the same process is difficult.
GRETL is a C++ library for evaluation, re-evaluation and algorithmic differentiation of functional operations on an arbitrary computational graph with limited memory usage. Similar to popular machine learning frameworks in Python, like PyTorch and JAX, it tracks and stores both operations and output data as functions are evaluated. Once this composition of functions is built up, the entire chain of operations can be back propagated to compute sensitivities of the final result with respect to any number of inputs. In contrast to most machine learning applications, memory usage becomes the bottleneck for back propagation in many physics applications, especially for time-dependent PDEs. Dynamic check pointing becomes essential. An important distinguishing feature of GRETL is its ability to limit the maximum memory usage by automatically dynamic checkpointing the data output for each graph operation (see Wang, Moin, Iaccarino, 2009). During backpropagation, parts of the graph that are no longer in memory are automatically re-evaluated from upstream checkpointed states as needed for derivative sensitivity calculations (or more precisely, for vector-Jacobian products). GRETL is particularly beneficial for applications, such as coupled multi-physics, where deriving adjoint-based sensitivities and managing checkpoint memory across modules becomes onerous. Cases which can be readily handled by the GRETL library include: different time-integration algorithms per physics (e.g., coupled predictor-corrector algorithms, IMEX, etc.), sub-cycling, asynchronous integrators, state dependent timestep sizes, iterative solvers and coupling algorithms, controller algorithms, and more.
Sphynx is a software library for parallel graph partitioning and load balancing. It partitions a set of vertices in a graph such that the vertex parts are balanced, and the edge cut is approximately minimized. The primary use case is to partition a computational graph into smaller tasks that can be assigned to processors (cores) for efficient parallel computing. Sphynx is based on the Trilinos scientific computing toolkit so can run on both multi-CPU and multi-GPU systems. SAND2020-12183 M Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.
X-ray fluorescence (XRF) is a popular spectroscopy technique for elemental analysis. Spectrum fitting and parameter tuning are at the core of XRF analysis and are conventionally manually intensive, especially for synchrotron experiments involving large amounts of diverse samples. This work introduces the automatic differentiation (AD) technique to XRF and an open-source package called MapsTorch. By transforming an analytical model of the XRF spectrum into a differentiable computation graph with AD, MapsTorch enables robust optimization of parameters and elemental intensities. We evaluate MapsTorch by conducting computational experiments on a large number of historical synchrotron XRF datasets and compare its performance with the currently practiced fitting tool NLopt. The results show that MapsTorch consistently achieves high-quality fits and often leads to better fitting quality than NLopt, particularly in tasks such as initial spectrum fitting and elemental intensity refinement. The robust performance of MapsTorch paves the way for developing automated and high-throughput XRF data analysis workflows to handle the increasing data volumes expected from next-generation synchrotron facilities.
The management of redundancy in computer systems was studied and guidelines were provided for the development of NASA's fault-tolerant distributed systems. Fault recovery and reconfiguration mechanisms were examined. A theoretical foundation was laid for redundancy management by efficient reconfiguration methods and algorithmic diversity. Algorithms were developed to optimize the resources for embedding of computational graphs of tasks in the system architecture and reconfiguration of these tasks after a failure has occurred. The computational structure represented by a path and the complete binary tree was considered and the mesh and hypercube architectures were targeted for their embeddings. The innovative concept of Hybrid Algorithm Technique was introduced. This new technique provides a mechanism for obtaining fault tolerance while exhibiting improved performance.
The fabric structure pictured is the Campus Center of La Verne College, La Verne, California. Unlike the facilities shown on the preceding pages, it is not air-supported. It is a "tension structure," its multi-coned fabric membrane supported by a network of cables attached to steel columns which function like circus tent poles. The spider-web in the accompanying photo is a computer graph of the tension pattern. The designers, Geiger-Berger Associates PC, of New York City, conducted lengthy computer analysis to determine the the best placement of columns and cables. The firm also served as structural engineering consultant on the Pontiac Silverdome and a number of other large fabric structures. Built by Birdair Structures, Inc., Buffalo, New York, the La Verne Campus Center was the first permanent facility in the United States enclosed by the space-spinoff fabric made of Owens-Corning Beta fiber glass coated with Du Pont Teflon TFE. The flexible design permits rearrangement of the interior to accommodate athletic events, student activities, theatrical productions and other recreational programs. Use of fabric covering reduced building cost 30 percent below conventional construction.
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.
Even though it is well known that binary values are common in graph applications (e.g., adjacency matrix), how to leverage the phenomenon for efficiency has not yet been adequately explored. This paper presents a systematic study on how to unlock the potential of the bit-level optimizations of graph computations that involve binary values. It proposes a two-level representation named Bit-Block Compressed Sparse Row (B2SR) and presents a series of optimizations to the graph operations on B2SR by the intrinsics of modern GPUs. It additionally introduces Deep Reinforcement Learning (DRL) as an efficient way to best configure the bit-level optimizations on the fly. Additionally, the DQN-based adaptive tile size selector with dedicated model training can reach 68% prediction accuracy. Evaluations on NVIDIA Pascal and Volta GPUs show that the optimizations bring up to 40× and 6555× for essential GraphBLAS kernels SpMV and SpGEMM, respectively, making GraphBLAS-based BFS accelerate up to 433×, SSSP, PR, and CC up to 35×, and TC up to 52×.