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All sources NASA NTRS DOE OSTI

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

nuclear-score-maximization v1.0

This software library presents efficient and multithreaded implementations of matrix low rank approximation via column selection in C++17 code. The algorithms are described in Fornace, Mark, and Michael Lindsey. "Column and row subset selection using nuclear scores: algorithms and theory for Nystro m approximation, CUR decomposition, and graph Laplacian reduction." arXiv preprint arXiv:2407.01698 (2024). The presented methods are by-and-large ver novel, have provable approximation guarantees, multiple use-cases, and exhibit higher quality approximations on a variety of studied examples.

Fornace, Mark↗

NASA NTRS1992

A system for verifying models and classification maps by extraction of information from a variety of data sources

Recent updates to a geographical information system (GIS) called VICAR (Video Image Communication and Retrieval)/IBIS are described. The system is designed to handle data from many different formats (vector, raster, tabular) and many different sources (models, radar images, ground truth surveys, optical images). All the data are referenced to a single georeference plane, and average or typical values for parameters defined within a polygonal region are stored in a tabular file, called an info file. The info file format allows tracking of data in time, maintenance of links between component data sets and the georeference image, conversion of pixel values to `actual' values (e.g., radar cross-section, luminance, temperature), graph plotting, data manipulation, generation of training vectors for classification algorithms, and comparison between actual measurements and model predictions (with ground truth data as input).

Norikane, L.↗

DOE OSTI2026

Classification of dynamical Lie algebras generated by spin interactions on undirected graphs

Dynamical Lie algebras (DLAs) are a versatile tool for various topics that span from the expressibility-trainability of variational quantum algorithms (VQAs), to simulation of many body Hamiltonians. Quantum gates and most of the Hamiltonians of interest consist of local interactions; therefore, the analysis of all possible DLAs generated by 1- and 2-local operators is crucial for quantum simulation and VQAs on current hardware. Previously in [R. Wiersema et al ., npj Quantum Inf. 10 , 110 (2024)], we analyzed the DLAs on linear, circular and all-to-all topologies, and obtained results about their dimensions and algebraic structure. Here, in this work, we extend our analysis into any possible hardware topology and provide a classification of all DLAs generated by Pauli strings on any undirected interaction graph. Our results indicate that the DLAs depend solely on whether the connectivity or interaction graph is bipartite or not. In addition, we find that the non-trivial polynomially scaling DLAs appear only on 1D line or circle topologies, and all other DLAs have dimensions scaling exponentially with the system size. Together with the current VQA literature, our results imply that either the majority of VQAs are non-trainable, or we are yet to understand the role of DLAs on the trainability of VQAs.

Algebraic structures↗

DOE OSTI2026

Graph Identification of Proteins in Tomograms (GRIP-Tomo) 2.0: Topologically aware classification for proteins

Cryo-electron tomography (cryo-ET) enables structural characterization of biomolecules under near-native conditions. Existing approaches for interpreting the resulting three-dimensional volumes are computationally expensive and have difficulty interpreting density associated with small proteins/complexes. To explore alternate approaches for identifying proteins in cryo-ET data we pursued a Graph Network and topologically invariant approach. Here, we report on a fast algorithm that classifies particles by searching for nuances of evolutionarily conversed motifs and the geometrical characteristics of protein structure. GRIP-Tomo 2.0 is a machine-learning pipeline that extracts interpretable topological features of protein structures within noisy experimental backgrounds. Compared to version 1.0, the new pipeline includes three upgrades that significantly improve performance including synthetic tomogram generation simulating realistic noise, graph-based persistent feature extraction as protein fingerprints, and high-performance computing acceleration. GRIP-Tomo 2.0 achieves over 90% accuracy in classifying between proteins and noise using both real and synthetic datasets which represents a foundational step toward advancing cryo-ET workflows and empowering automated visual proteomics.

Li, Chengxuan↗

NASA NTRS2002

Reducing False Positives in Runtime Analysis of Deadlocks

This paper presents an improvement of a standard algorithm for detecting dead-lock potentials in multi-threaded programs, in that it reduces the number of false positives. The standard algorithm works as follows. The multi-threaded program under observation is executed, while lock and unlock events are observed. A graph of locks is built, with edges between locks symbolizing locking orders. Any cycle in the graph signifies a potential for a deadlock. The typical standard example is the group of dining philosophers sharing forks. The algorithm is interesting because it can catch deadlock potentials even though no deadlocks occur in the examined trace, and at the same time it scales very well in contrast t o more formal approaches to deadlock detection. The algorithm, however, can yield false positives (as well as false negatives). The extension of the algorithm described in this paper reduces the amount of false positives for three particular cases: when a gate lock protects a cycle, when a single thread introduces a cycle, and when the code segments in different threads that cause the cycle can actually not execute in parallel. The paper formalizes a theory for dynamic deadlock detection and compares it to model checking and static analysis techniques. It furthermore describes an implementation for analyzing Java programs and its application to two case studies: a planetary rover and a space craft altitude control system.

Bensalem, Saddek↗

NASA NTRS1993

A spectral algorithm for envelope reduction of sparse matrices

A new algorithm for reducing the envelope of a sparse matrix is presented. This algorithm is based on the computation of eigenvectors of the Laplacian matrix associated with the graph of the sparse matrix. A reordering of the sparse matrix is determined based on the numerical values of the entries of an eigenvector of the Laplacian matrix. Numerical results show that the new reordering algorithm can in some cases reduce the envelope by more than a factor of two over the current standard algorithms such as Gibbs-Poole-Stockmeyer (GPS) or SPARSPAK's reverse Cuthill-McKee (RCM).

Barnard, Stephen T.↗

DOE OSTI2024

SNNVis: Visualizing Graph Embedding of Evolutionary Optimization for Spiking Neural Networks

While Spiking Neural Networks (SNNs) show a lot of promise, it is difficult to optimize them because applying traditional gradient-based optimization techniques is difficult. Even though evolutionary algorithms (EAs) have been shown to promise to optimize SNNs, understanding the relationship between evolving the characteristics of SNNs and their performance to improve the optimization algorithm is challenging because of the complex characteristics and huge population size. We propose visual analytics with novel graph embedding for evolutionary SNNs to address the challenges. While existing graph embedding techniques have limitations in preserving the specific features of the nodes and edges, our approach maintains them. Also, we develop visual analytics for understanding the relationship between the network performance and the features of nodes and edges and exploring and analyzing the evolving SNNs to build insights into improving the EA.

Chae, Junghoon [ORNL] (ORCID:0000000206016746)↗

DOE OSTI2026

buhito

buhito is a Python library for graph analysis and machine learning. Graphs can represent networks with objects as nodes and their relationships as edges. buhito focuses on graphlet methods that study graphs through enumerating their component subgraphs to enable interpretable and fast models of complex systems. The package provides tools for different algorithmic designs for computing, analyzing, and applying graphlets to research problems such as machine learning, data compression, and anomaly detection in graph-structured data. A central feature is performing decomposition data analysis on graphs for machine learning models. Implemented in Python and built upon open-source scientific libraries such as NetworkX, NumPy, and SciPy, buhito provides high-performance methods for researchers exploring the mathematical and computational foundations of graphlet analysis applicable to systems of different sizes.

Pimonova, Yulia↗

NASA NTRS1994

Aligning parallel arrays to reduce communication

Axis and stride alignment is an important optimization in compiling data-parallel programs for distributed-memory machines. We previously developed an optimal algorithm for aligning array expressions. Here, we examine alignment for more general program graphs. We show that optimal alignment is NP-complete in this setting, so we study heuristic methods. This paper makes two contributions. First, we show how local graph transformations can reduce the size of the problem significantly without changing the best solution. This allows more complex and effective heuristics to be used. Second, we give a heuristic that can explore the space of possible solutions in a number of ways. We show that some of these strategies can give better solutions than a simple greedy approach proposed earlier. Our algorithms have been implemented; we present experimental results showing their effect on the performance of some example programs running on the CM-5.

Sheffler, Thomas J.↗

DOE OSTI2025

OpenSn: A massively parallel, open-source simulation environment for discrete ordinates radiation transport

OpenSn is an open-source, massively parallel deterministic radiation transport code for solving the discrete-ordinates ( S N ) form of the Boltzmann transport equation on unstructured, arbitrary polyhedral meshes. It supports high-fidelity simulations involving steady-state, eigenvalue, and adjoint problems for neutral particles (e.g., neutrons, photons, multi-particles), using the multigroup approximation in energy. OpenSn combines angular discretization via discrete ordinates with a discontinuous Galerkin finite element method (DGFEM) in space, enabling accurate resolution of transport physics on arbitrary polyhedral cells, included locally refined spatial grids. It includes multiple angular quadrature types, including locally refined angular quadratures. Written in modern C++ with a Python API, OpenSn runs efficiently on platforms ranging from laptops to supercomputers. The transport sweep algorithm is implemented using a task-based, directed-acyclic-graph (DAG) approach for each angle and supports asynchronous parallelism across thousands of MPI ranks. Group-set aggregation improves compute intensity, and synthetic acceleration techniques (e.g., diffusion synthetic acceleration, second-moment method) enhance solver convergence. OpenSn has been verified on reactor physics problems and demonstrated excellent weak and strong scaling performance on more than 32,768 processes, making it a versatile and robust platform for large-scale transport simulations in complex geometries.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Predicting Band-Gap of Inorganic Materials Using Neuromorphic Graph Learning

Predicting properties of inorganic materials is a heavily researched topic, with several new prediction approaches emerging as competitors. One such competitor is graph neural networks, which leverage the structure of the graph to aid in the prediction process. In this work, we propose integration of neuromorphic computation into the graph neural network pipeline. We call this approach Neuromorphic Graph Learning (NGL). We utilize the NGL approach to leverage evolutionary algorithms and a novel Spike Pipeline for Raster Analysis (SPIRE) for the prediction of band gap in inorganic materials.

Mulet, Ian [University of Tennessee (UT)]↗

NASA NTRS1995

Learning In networks

Intelligent systems require software incorporating probabilistic reasoning, and often times learning. Networks provide a framework and methodology for creating this kind of software. This paper introduces network models based on chain graphs with deterministic nodes. Chain graphs are defined as a hierarchical combination of Bayesian and Markov networks. To model learning, plates on chain graphs are introduced to model independent samples. The paper concludes by discussing various operations that can be performed on chain graphs with plates as a simplification process or to generate learning algorithms.

Buntine, Wray L.↗

NASA NTRS2022

Real-World Testing of LiDAR-Inertial Based Navigation and Mapping for Precision Landing

The fusion of LiDAR and inertial measurements duringspacecraft descent and landing can be used to estimate alander’s navigation state and map the terrain below. Together,these data products can be used to enable safe and preciselanding on celestial bodies for which a priori orbital reconnaissanceis insufficient for hazard detection and avoidance.Unlike camera images used in visual terrain relative navigation,LiDAR scans are insensitive to changes in illumination; as aresult, the technique can be used to land in poorly lit areas,or at times of day when the lighting conditions are incongruentwith existing orbital imagery. In this paper, we extend previouswork in which we introduced a factor graph based smoothingapproach for LiDAR-inertial navigation and mapping. Whereasthe algorithms were previously tested on simulated data, thispaper presents testing on real-world data. Data from theAutonomous Landing Hazard Avoidance Technology (ALHAT)airplane flight tests in the Yucca Flats and Death Valley in2009 (FT3), the Morpheus vertical take off and landing flighttests at Kennedy Space Center in 2014 (FT6), and the landingof Perseverance and Ingenuity on Mars in 2021 (M2020) wereused to evaluate algorithm performance. In this paper, weextend our LiDAR-inertial technique to work with a variety ofranging technologies: single point laser altimetry (FT3), denseflash LiDAR (FT6), and six-beam radar (M2020). A thoroughperformance analysis for all three datasets is presented. Datasetpreparation, improvements in algorithm robustness, and outlierrejection, which were necessitated by the transition to realworlddata, are discussed.

Trawny, Nikolas↗

NASA NTRSDate not supplied

Automated Multi-Robot Assembly of Compliance Optimized Structures

Autonomous assembly of large structures is one of the fundamental challenges on the way towards NASA’s objectives of deep space exploration. In this work, we propose an algorithmic framework to optimize the assembly process of a prescribed target structure by constraining the assembly effort as well as maintaining structural soundness throughout the process. This framework uses structural topology optimization with assembly effort metrics to generate checkpoints for robotic traversal algorithms. Assembly effort is quantified by the Wasserstein metric between consecutive structural configurations during the assembly process. The robotic assembly task is split into two subtasks, where we first optimize for a set of key frames, then perform reconfiguration between consecutive frames. Key frames are optimized by adopting topology optimization techniques to reduce assembly effort and maintain structural integrity during the assembly process, while reconfiguration between key frames is performed using a path planning algorithm with a minimum weight maximum matching approach on a bipartite graph. We employ a Crystalline robot model in which each structural element is capable of locomotion through the structure and locking into place with neighboring elements after reaching its destination. An example assembly of a two-dimensional cantilever beam under volume constraints and structural compliance considerations is presented to demonstrate the approach. Finally, we conclude by discussing possible future extensions to this work, including adoption of better metrics, extension to three-dimensional large-scale problems, and exacting finer control of structural integrity during the path-planning phase.

robotic assembly↗

NASA NTRS1992

Fault detection and initial state verification by linear programming for a class of Petri nets

The authors present an algorithmic approach to determining when the marking of a LSMG (live safe marked graph) or a LSFC (live safe free choice) net is in the set of live safe markings M. Hence, once the marking of a net is determined to be in M, then if at some time thereafter the marking of this net is determined not to be in M, this indicates a fault. It is shown how linear programming can be used to determine if m is an element of M. The worst-case computational complexity of each algorithm is bounded by the number of linear programs necessary to compute.

Rachell, Traxon↗

NASA NTRS2021

Small UAV Flight Planning in Urban Environments

This work proposes a fast algorithm for generating obstacle-free and wind-efficient flight paths at a constant above-ground-level altitude in urban environments because a fast flight path planning algorithm is an essential function or service needed for enabling small unmanned aerial vehicle (sUAV) to operate in urban environments within Class G airspace. The proposed method first converts the 3D path planning problem to a 2D problem by constructing an obstacle map at a given above-ground-level altitude. A quad-tree decomposition is then used to build a search space in terms of obstacle occupancy and wind difference. The wind cost of traveling through each cell is defined based on energy consumption under various wind conditions. A repulsive potential is also adopted to make sure that the flight plans stay away from obstacles. The Theta* search algorithm, a variant of A* algorithm, is applied to mitigate the path angle change constraints introduced by grid-based graphs. With the Theta* and postsmoothing techniques, an obstacle-free, wind efficient, and constant above-ground-level flight plan can be quickly generated for sUAV operations in urban environments while meeting the lateral path angle constraints. The results showed that the path planning algorithm is efficient and can be finished within several seconds. With a proper choice of wind coefficient, the proposed path planning algorithm outperforms the multiple-shooting trajectory optimization method even in an obstacle-free environment. With the flexibility of incorporating other geo-related costs and computation efficiency, the proposed algorithm shows the potential for real-time flight path planning in complex urban environments.

Path planning↗

DOE OSTI2025

ARCH: Large-scale knowledge graph via aggregated narrative codified health records analysis

Objective: Electronic health record (EHR) systems contain a wealth of clinical data stored as both codified data and free-text narrative notes (NLP). The complexity of EHR presents challenges in feature representation, information extraction, and uncertainty quantification. Here, to address these challenges, we proposed an efficient Aggregated naRrative Codified Health (ARCH) records analysis to generate a large-scale knowledge graph (KG) for a comprehensive set of EHR codified and narrative features. Methods: Using data from 12.5 million Veterans Affairs patients, ARCH first derives embedding vectors and generates similarities along with associated p-values to measure the strength of relatedness between clinical features with statistical certainty quantification. Next, ARCH performs a sparse embedding regression to remove indirect linkage between features to build a sparse KG. Finally, ARCH was validated on various clinical tasks, including detecting known relationships between entity pairs, predicting drug side effects, disease phenotyping, as well as sub-typing Alzheimer’s disease patients. Results: ARCH produces high-quality clinical embeddings and KG for over 60,000 codified and narrative EHR concepts. The KG and embeddings are visualized in the R-shiny powered web-API.3 ARCH achieved high accuracy in detecting EHR concept relationships, with AUCs of 0.926 (codified) and 0.861 (NLP) for similar EHR concepts, and 0.810 (codified) and 0.843 (NLP) for related pairs. It detected drug side effects with a 0.723 AUC, which improved to 0.826 after fine-tuning. Using both codified and NLP features, the detection power increased significantly. Compared to other methods, ARCH has superior accuracy and enhances weakly supervised phenotyping algorithms’ performance. Notably, it successfully categorized Alzheimer’s patients into two subgroups with varying mortality rates. Conclusion: The proposed ARCH algorithm generates large-scale high-quality semantic representations and knowledge graph for both codified and NLP EHR features, useful for a wide range of predictive modeling tasks.

Electronic health records↗