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DOE OSTI2025

PySIDT: Subgraph Isomorphic Decision Trees for Molecular Property Prediction

Accurate molecular property prediction is important across all fields of chemistry. Deep neural networks (DNNs) have become increasingly popular due to their ability to train automatically, avoiding the incredibly tedious process of constructing and extending traditional property estimation schemes. However, DNNs require large amounts of training data, are challenging to interpret, require large amounts of memory to load even during inference, and have severe difficulties incorporating qualitative chemical knowledge, which are often desired for molecular property prediction tasks. Here, in this study, we present PySIDT (https://github.com/zadorlab/PySIDT), a software for training and running inference on Subgraph Isomorphic Decision Trees (SIDTs). SIDTs are graph-based decision trees made of nodes associated with molecular substructures. Inference is done by descending target molecular structures down the decision tree to nodes with matching subgraph isomorphic substructures and making predictions based on the final (most specific) nodes matched. SIDTs scale down well to dataset sizes much smaller than is feasible for DNNs. As trees of molecular substructures, SIDTs are inherently readable and easy to visualize, making them easy to analyze. They are also straightforward to extend and retrain, facilitate uncertainty estimation, and enable easy integration of expert knowledge. We demonstrate the SIDT approach discussing its application to a diverse range of molecular prediction tasks: rate coefficient estimation, diffusion coefficient estimation, thermochemistry estimation, transition state bond stretch prediction, p K a prediction, stability of molecular structures, stability of surface structures, and prediction of surface lateral interaction energetics. Additionally, we demonstrate the power of the SIDT algorithms in two direct learning curve vanilla comparisons with the popular DNN-based software Chemprop and the popular gradient boosted trees-based software XGBoost on enthalpy of formation and rate coefficient prediction tasks. In particular, in the enthalpy of formation case, vanilla PySIDT is able to outperform vanilla Chemprop and XGBoost across the full range of training/validation set sizes out to 11,560 data points.

Johnson, Matthew Sean [Sandia National Laboratorie↗

DOE OSTI2020

Faster Johnson–Lindenstrauss transforms via Kronecker products

The Kronecker product is an important matrix operation with a wide range of applications in signal processing, graph theory, quantum computing and deep learning. In this work, we introduce a generalization of the fast Johnson–Lindenstrauss projection for embedding vectors with Kronecker product structure, the Kronecker fast Johnson–Lindenstrauss transform (KFJLT). The KFJLT reduces the embedding cost by an exponential factor of the standard fast Johnson–Lindenstrauss transform’s cost when applied to vectors with Kronecker structure, by avoiding explicitly forming the full Kronecker products. Here, we prove that this computational gain comes with only a small price in embedding power: consider a finite set of $p$ points in a tensor product of $d$ constituent Euclidean spaces $\bigotimes _{k=d}^{1}{\mathbb{R}}^{n_k}$, and let $N = \prod _{k=1}^{d}n_k$. With high probability, a random KFJLT matrix of dimension $m \times N$ embeds the set of points up to multiplicative distortion $(1\pm \varepsilon )$ provided $m \gtrsim \varepsilon ^{-2} \, \log ^{2d - 1} (p) \, \log N$. We conclude by describing a direct application of the KFJLT to the efficient solution of large-scale Kronecker-structured least squares problems for fitting the CP tensor decomposition.

Kronecker structure↗

NASA NTRS1993

Effects of flow-path variations on internal reversing flow in a tailpipe offtake configuration for ASTOVL aircraft

A one-third-scale model of a generic tailpipe offtake system for an advanced short takeoff, vertical landing (ASTOVL) aircraft was tested at the NASA Lewis Research Center Powered Lift Facility. The basic model consisted of a tailpipe with a center body to form an annulus simulating turbine outflow with no swirl; twin offtake ducts with elbows at the ends to turn the flow to a downward direction; flow control nozzles at the ends of the elbows; and a blind flange at the end of the tailpipe to simulate a closed cruise nozzle. The offtake duct-to-tailpipe diameter ratio was 0.74. Modifications of a generic nature were then made to this basic configuration to measure the effects of flow-path changes on the flow and pressure-loss characteristics. The modifications included adding rounded entrances at the forward edges of the offtake openings, blocking the tailpipe just aft the openings instead of at the cruise nozzle, changing the location of the openings along the tailpipe, removing the center body, and varying the Mach number (flow rate) over a wide range in the tailpipe ahead of the openings by changing the size of the flow control nozzles. The tests were made with unheated air at tailpipe-to-ambient pressure ratios from 1.4 to 5. Results are presented and compared with performance graphs, total-pressure contour plots, paint streak flow visualization photographs, and a flow-angle probe traverse at the offtake entrance.

Mcardle, Jack G.↗

NASA NTRS1993

Effects of flow-path variations on internal reversing flow in a tailpipe offtake configuration for ASTOVL aircraft

Mcardle, Jack G.↗

DOE OSTI2026

NuGraph2 with context-aware inputs: physics-inspired improvements in semantic segmentation

Graph neural networks have recently shown strong promise for event reconstruction tasks in Liquid Argon Time Projection Chambers, yet their performance remains limited for underrepresented classes of particles, such as Michel electrons. In this work, we investigate physics-informed strategies to improve semantic segmentation within the NuGraph2 architecture. We explore three complementary approaches: (i) enriching the input representation with context-aware features derived from detector geometry and track continuity, (ii) introducing auxiliary decoders to capture class-level correlations, and (iii) incorporating energy-based regularization terms motivated by Michel electron energy distributions. Experiments on MicroBooNE public datasets show that physics-inspired feature augmentation yields the largest gains, particularly boosting Michel electron precision and recall by disentangling overlapping latent space regions. In contrast, auxiliary decoders and energy-regularization terms provided limited improvements, partly due to the hit-level nature of NuGraph2, which lacks explicit particle- or event-level representations. Our findings highlight that embedding physics context directly into node-level inputs is more effective than imposing task-specific auxiliary losses, and suggest that future hierarchical architectures such as NuGraph3, with explicit particle- and event-level reasoning, will provide a more natural setting for advanced decoders and physics-based regularization. The code for this work is publicly available on Github at https://github.com/vitorgrizzi/nugraph_phys/tree/main_phys.

Other Experiments↗

NASA NTRS1994

A genetic technique for planning a control sequence to navigate the state space with a quasi-minimum-cost output trajectory for a non-linear multi-dimnensional system

There are many multi-stage optimization problems that are not easily solved through any known direct method when the stages are coupled. For instance, we have investigated the problem of planning a vehicle's control sequence to negotiate obstacles and reach a goal in minimum time. The vehicle has a known mass, and the controlling forces have finite limits. We have developed a technique that finds admissible control trajectories which tend to minimize the vehicle's transit time through the obstacle field. The immediate applications is that of a space robot which must rapidly traverse around 2-or-3 dimensional structures via application of a rotating thruster or non-rotating on-off for such vehicles is located at the Marshall Space Flight Center in Huntsville Alabama. However, it appears that the development method is applicable to a general set of optimization problems in which the cost function and the multi-dimensional multi-state system can be any nonlinear functions, which are continuous in the operating regions. Other applications included the planning of optimal navigation pathways through a transversability graph; the planning of control input for under-water maneuvering vehicles which have complex control state-space relationships; the planning of control sequences for milling and manufacturing robots; the planning of control and trajectories for automated delivery vehicles; and the optimization and athletic training in slalom sports.

Hein, C.↗

DOE OSTI2021

Dark moments for the Standard Model?

If dark matter (DM) interacts with the Standard Model (SM) via the kinetic mixing (KM) portal, it necessitates the existence of portal matter (PM) particles which carry both dark and SM quantum numbers that will appear in vacuum polarization-like loop graphs. In addition to the familiar ~ eϵQ strength, QED-like interaction for the dark photon (DP), in some setups different loop graphs of these PM states can also induce other coupling structures for the SM fermions that may come to dominate in at least some regions of parameter space regions and which can take the form of ‘dark’ moments, e.g., magnetic dipole-type interactions in the IR, associated with a large mass scale, Λ. In this paper, motivated by a simple toy model, we perform a phenomenological investigation of a possible loop-induced dark magnetic dipole moment for SM fermions, in particular, for the electron. We show that at the phenomenological level such a scenario can not only be made compatible with existing experimental constraints for a significant range of correlated values for Λ and the dark U(1) D gauge coupling, g D , but can also lead to quantitatively different signatures once the DP is discovered. In this setup, assuming complex scalar DM to satisfy CMB constraints, parameter space regions where the DP decays invisibly are found to be somewhat preferred if PM mass limits from direct searches at the LHC and our toy model setup are all taken seriously. High precision searches for, or measurements of, the e + e - → γ + DP process at Belle II are shown to provide some of the strongest future constraints on this scenario.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

A change language for ontologies and knowledge graphs

Ontologies and knowledge graphs (KGs) are general-purpose computable representations of some domain, such as human anatomy, and are frequently a crucial part of modern information systems. Most of these structures change over time, incorporating new knowledge or information that was previously missing. Managing these changes is a challenge, both in terms of communicating changes to users and providing mechanisms to make it easier for multiple stakeholders to contribute. To fill that need, we have created KGCL, the Knowledge Graph Change Language (https://github.com/INCATools/kgcl), a standard data model for describing changes to KGs and ontologies at a high level, and an accompanying human-readable Controlled Natural Language (CNL). This language serves two purposes: a curator can use it to request desired changes, and it can also be used to describe changes that have already happened, corresponding to the concepts of “apply patch” and “diff” commonly used for managing changes in text documents and computer programs. Another key feature of KGCL is that descriptions are at a high enough level to be useful and understood by a variety of stakeholders—e.g. ontology edits can be specified by commands like “add synonym ‘arm’ to ‘forelimb’” or “move ‘Parkinson disease’ under ‘neurodegenerative disease’.” We have also built a suite of tools for managing ontology changes. These include an automated agent that integrates with and monitors GitHub ontology repositories and applies any requested changes and a new component in the BioPortal ontology resource that allows users to make change requests directly from within the BioPortal user interface. Overall, the KGCL data model, its CNL, and associated tooling allow for easier management and processing of changes associated with the development of ontologies and KGs.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

DOE OSTI2024

How the Galaxy–Halo Connection Depends on Large-scale Environment

We investigate the connection between galaxies, dark matter halos, and their large-scale environments at z = 0 with Illustris TNG300 hydrodynamic simulation data. We predict stellar masses from subhalo properties to test two types of machine learning (ML) models: explainable boosting machines (EBMs) with simple galaxy environment features and E(3)-invariant graph neural networks (GNNs). The best-performing EBM models leverage spherically averaged overdensity features on 3 Mpc scales. Interpretations via SHapley Additive exPlanations also suggest that in the context of the TNG300 galaxy–halo connection, simple spherical overdensity on ∼3 Mpc scales is more important than cosmic web distance features measured using the DisPerSE algorithm. Meanwhile, a GNN with connectivity defined by a fixed linking length, L, outperforms the EBM models by a significant margin. As we increase the linking length scale, GNNs learn important environmental contributions up to the largest scales we probe (L = 10 Mpc). We conclude that 3 Mpc distance scales are most critical for describing the TNG galaxy–halo connection using the spherical overdensity parameterization, but that information on larger scales, which is not captured by simple environmental parameters or cosmic web features, can further augment these models. Our study highlights the benefits of using interpretable ML algorithms to explain models of astrophysical phenomena, and the power of using GNNs to flexibly learn complex relationships directly from data while imposing constraints from physical symmetries.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Understanding the effect of density functional choice and van der Waals treatment on predicting the binding configuration, loading, and stability of amine-grafted metal organic frameworks

Metal organic frameworks (MOFs) are crystalline, three-dimensional structures with high surface areas and tunable porosities. Made from metal nodes connected by organic linkers, the exact properties of a given MOF are determined by node and linker choice. MOFs hold promise for numerous applications, including gas capture and storage. M2(4,4′-dioxidobiphenyl-3,3′-dicarboxylate)—henceforth simply M2(dobpdc), with M = Mg, Mn, Fe, Co, Ni, Cu, or Zn—is regarded as one of the most promising structures for CO2 capture applications. Further modification of the MOF with diamines or tetramines can significantly boost gas species selectivity, a necessity for the ultra-dilute CO2 concentrations in the direct-air capture of CO2. There are countless potential diamines and tetramines, paving the way for a vast number of potential sorbents to be probed for CO2 adsorption properties. The number of amines and their configuration in the MOF pore are key drivers of CO2 adsorption capacity and kinetics, and so a validation of computational prediction of these quantities is required to suitably use computational methods in the discovery and screening of amine-functionalized sorbents. In this work, we study the predictive accuracy of density functional theory and related calculations on amine loading and configuration for one diamine and two tetramines. In particular, we explore the Perdew–Burke–Ernzerhof (PBE) functional and its formulation for solids (PBEsol) with and without the Grimme-D2 and Grimme-D3 pairwise corrections (PBE+D2/3 and PBEsol+D2/3), two revised PBE functionals with the Grimme-D2 and Grimme-D3 pairwise corrections (RPBE+D2/3 and revPBE+D2/3), and the nonlocal van der Waals correlation (vdW-DF2) functional. We also investigate a universal graph deep learning interatomic potential’s (M3GNet) predictive accuracy for loading and configuration. These results allow us to identify a useful screening procedure for configuration prediction that has a coarse component for quick evaluation and a higher accuracy component for detailed analysis. Our general observation is that the neural network-based potential can be used as a high-level and rapid screening tool, whereas PBEsol+D3 gives a completely qualitatively predictive picture across all systems studied, and can thus be used for high accuracy motif predictions. We close by briefly exploring the predictions of relative thermal stability for the different functionals and dispersion corrections.

Chemistry↗

NASA NTRS2000

Power Systems Evaluated for Solar Electric Propulsion Vehicles

Solar electric propulsion (SEP) mission architectures are applicable to a wide range NASA missions including the robotic exploration of the outer planets in the next decade and the human exploration of Mars within the next 2 decades. SEP enables architectures that are very mass efficient with reasonable power levels (1-MW class) aerobrake and cryogenic upper-stage transportation technologies are utilized. In this architecture, the efficient SEP stage transfers the payload from low Earth orbit (LEO) High Energy Elliptical Parking Orbit (HEEPO) within a period of 6 to 12 months. highthrust, cryogenic upper stage and payload then separate from the SEP vehicle for injection to the planetary target, allowing for fast heliocentric trip times. This mission architecture offers a potential reduction in mass to LEO in comparison to alternative all-chemical nuclear propulsion schemes. Mass reductions may allow launch vehicle downsizing enable missions that would have been grounded because of cost constraints. The preceding figure illustrates a conceptual SEP stage design for a human Mars mission. Researchers at the NASA Glenn Research Center at Lewis Field designed conceptual SEP vehicle, conceived the mission architecture to use this vehicle, and analyzed the vehicle s performance. This SEP stage has a dry mass of 35 metric tons (MT), 40 MT of xenon propellant, and a photovoltaic array that spans 110 m, providing power to a cluster of eight 100-kW Hall thrusters. The stage can transfer an 80-MT payload and upper stage to the desired HEEPO. Preliminary packaging studies show this space-station-class SEP vehicle meets the proposed "Magnum" launch vehicle and volume requirements with considerable margin. An SEP vehicle for outer planetary missions, such as the Europa Mapper Mission, would be dramatically smaller than human Mars mission SEP stage. In this mission architecture, the SEP power system with the payload to provide spacecraft power throughout the mission. Several photovoltaic array design concepts were considered for the SEP vehicle power system for the human mission to Mars. These include a space station derivative, a SCARLET (Solar Concentrator Arrays with Refractive Linear Element Technology) derivative, and a hybrid inflatable-deployable thin polymer membrane array with thin-film solar cells (as shown in the concept illustration). This concept is based on a design developed for the Next Generation Space Telescope Sun shield. The array is divided into 16 independent electrical sections with 500-V, negative-grounded solar cell strings. The power system employs a channelized, 500-Vdc power management and distribution (PMAD) architecture with lithium ion batteries for energy storage for vehicle and payload secondary loads (the high-power Hall thrusters do not operate in eclipse periods). The 500-V PMAD voltage permits "direct-drive" thruster operation, greatly reducing the power processing unit size, complexity, and power loss. Similar power system architecture, designs, and technology are assumed for the Europa Mapper Mission SEP vehicle. The primary exceptions are that the photovoltaic array is assumed to consist of two rectangular wings and that the power system rating is 15 kW in Earth orbit and 200 W at Europa. To size the SEP vehicle power system, a dedicated Fortran code was developed to predict detailed power system performance, mass, and thermal control requirements. This code also modeled all the relevant Earth orbit environments; that is, the particulate radiation, plasma, meteoroids and debris, ultraviolet radiation, contamination, and thermal conditions. Analysis results for the Human Mars Mission SEP vehicle show a power system mass of 9-MT and photovoltaic array area of 5800-square meters for the thin-membrane design concept with CuInS2 thin-film cells. Power processing unit input power for a thin-membrane array design with three-junction, amorphous SiGe solar cells is shown in the graph. Power falls off rapidly inhe first weeks of the mission because of light-induced (Staebler-Wronksi) solar cell losses. During the next 200 days, power decreases steadily as the SEP stage spirals through the proton belts and sustains the bulk of the mission radiation damage. Once the vehicle apogee is above approximately four Earth radii, little additional degradation is incurred. From 400 to 800 days, a 1100-km "parking" orbit is maintained to await the next payload transfer opportunity. This orbit is below the main proton belt, and thus, little radiation dose is accumulated during this time period. During the second LEO-to-HEEPO transfer, power degrades somewhat further, but power requirements are still met. In comparison, the Europa Mapper SEP vehicle power system had a mass of 150 kg and a thin membrane array area of 100 square meters.

Kerslake, Thomas W.↗

NASA NTRS2001

Organization of P, S, and Fe Inclusions in a Freshwater Magnetococcus

Magnetotactic bacteria are a heterogeneous group of motile, mainly aquatic procaryotes that align and swim along geomagnetic field lines. They are of interest to astrobiologists because of the magnetite crystals found in the Mars meteorite ALH84001 which share many characteristics with the magnetite produced intracellularly by magnetotactic bacteria. These bacteria are diverse morphologically, physiologically and phylogenetically, sharing a few key characteristics: 1) the presence of intracellular membrane-bound magnetic crystals (magnetosomes), usually but not always arranged in chains; 2) motility by means of flagella; and 3) microaerophillic or anaerobic physiology. The bilophotrichous (having two flagella bundles) magnetotactic cocci (MC) are ubiquitous in aquatic habitats but have proven extremely difficult to cultivate. Because only several marine strains have been isolated and grown in axenic culture, little is known about the physiology and the biogeochemical roles of the MC. We studied the composition and distribution of intracellular structures in an uncultured MC, designated ARB-1. To do this, a combination of light microscopy, environmental scanning electron microscopy (ESEM), transmission electron microscopy (TEM) and energy dispersive X-ray spectroscopy (EDS) were used. Cells of ARB-1 were separated from sediments collected from Baldwin Lake (Los Angeles Arboretum, Arcadia, CA). They are large spherical to oblate spheroidal Gram-negative cells, ranging from 1 to 4 micrometers along the maximum dimension, which is perpendicular to the direction of swimming. Cells have two large phosphorus-containing inclusions that comprise a large percentage of the cell volume. Many smaller sulfur inclusions are located at the convex end of the cell. Most of the cellular Fe is present in the magnetosomes. These may be arranged as a clump at the concave end of the cell, near the two flagella bundles, or as chains, or as both a clump and chains. The magnetosomes were identified as magnetite (Fe3O4) by selected area electron diffraction (SAED) and high resolution TEM. We saw a trend between cell size and organization of the magnetosomes. Smaller, more spherical cells were more likely to have chains than were larger, more oblate cells. This may indicate different populations of cells, or it may be attributed to variations in cell growth cycle. The size distribution (length) of magnetosomes in chains was similar to that of magnetosomes in clusters, except that there was a larger size range for clustered magnetosomes. Magnetosomes from ARB-1 cells average 82 nm in length. If plotted on a graph of length as a function of aspect ratio, they fall within the single domain region of the plot. If compared with the size distributions of magnetite from ALH84001 and magnetosomes from the cultured magnetotactic vibrio MV-1, the magnetites produced by ARB-1 cells are, on average, larger and have a wider range of aspect ratio. ARB-1 cells have a specific organization of the P, S, and Fe inclusions. The P inclusions always occupy the majority of the cell volume and separate the S inclusions from the disorganized clumps of magnetosomes and the flagella bundles. The P inclusions may contain polyphosphate, which could play several roles in motility, adaptation to stress, growth and division, buoyancy, and energy. The S inclusions might be a way to store S, a potential energy source, when the cells move from sulfide to oxygen zones. The consistency of P, S, and Fe organization in ARB-1 cells suggests that these inclusions have some specific and interactive functions.

Cox, Lea↗

DOE OSTI2025

Replace Human Intelligence with Fast and Smart Geometric Reasoning and Graph Neural Network to Accelerate Next Gen ModSim Workflows

We present an agent-guided approach to CAD geometry decomposition that automates hex/hybrid meshing with graph neural networks (GNNs) to accelerate next-generation ModSim workflows. Our end-to-end pipeline (i) reduces 3D boundary-representation (B-Rep) models to a 2D chordal axis skeleton (CAT) and then to a 1D bipartite graph of surface and curve nodes, (ii) assigns per node labels as Cubit® WebCut actions, (iii) trains a multi-action GNN under supervised learning, and (iv) predicts five surface-node and three curve-node actions on out-of-distribution test geometries. Each graph node carries geometric, topological, and meshing attributes drawn from the B-Rep “skin” and CAT “skeleton,” with two-way mappings across 3D↔2D↔1D representations to maintain traceability back to 3D CAD. The supervised learning model exhibits stable convergence of the binary cross-entropy loss and achieves 98.7% accuracy on unseen lattice models. To operationalize decision-making, we rank predicted commands by geometric significance and prototyped the agent-guided workflow through the Cubit® Meshing PowerTool GUI. As a stretch goal, we explore reinforcement learning (RL) to reduce or remove label requirements and to learn policies for action sequences that maximize total reward (e.g., size of hex-meshable regions and resulting hex mesh quality). When all-hex meshing is not feasible, the agent assists in producing hybrid meshes—prioritizing hex in critical regions and transitioning to tetrahedral elements (tets) elsewhere—maintaining fidelity while ensuring robustness. The overarching objective is to replace manual, heuristics-based decomposition with data-driven, reproducible automation, cutting meshing turnaround time by orders of magnitude. We anticipate direct impact on simulation workflows through intelligent, scalable decomposition of complex CAD models into hex-meshable subdomains.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Closing the Loop between In Situ Stress Complexity and EGS Fracture Complexity

42 ENGINEERING↗

DOE OSTI2021

RivGraph: Automatic extraction and analysis of river and delta channel network topology

River networks sustain life and landscapes by carrying and distributing water, sediment, and nutrients throughout ecosystems and communities. At the largest scale, river networks drain continents through tree-like tributary networks. At typically smaller scales, river deltas and braided rivers form loopy, complex distributary river networks via avulsions and bifurcations.In order to model flows through these networks or analyze network structure, the topology, or connectivity, of the network must be resolved. Additionally, morphologic properties of each river channel as well as the direction of flow through the channel inform how fluxes travel through the network’s channels. Riv Graphis a Python package that automates the extraction and characterization of river channel networks from a user-provided binary image, or mask, of a channel network (Fig. 1). Masks may be derived from (typically remotely-sensed) imagery, simulations, or even hand-drawn. RivGraph will create explicit representations of the channel network by resolving river centerlines as links, and junctions as nodes. Flow directions are solved for each link of the network without using auxiliary data, e.g., a digital elevation model (DEM). Morphologic properties are computed as well, including link lengths, widths, sinuosities, branching angles,and braiding indices. If provided,RivGraph will preserve georeferencing information of the mask and will export results as ESRI shapefiles, GeoJSONs, and GeoTIFFs for easy import into GIS software.RivGraph can also return extracted networks as networkx objects for convenient interfacing with the full-featured networkx package (Hagberg et al., 2008). Finally, RivGraph offers a suite of topologic metrics that were specifically designed for river channel network analysis (Tejedor et al., 2015b).

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Probing for the Trace Estimation of a Permuted Matrix Inverse Corresponding to a Lattice Displacement

We report thatpProbing is a general technique that is used to reduce the variance of the Hutchinson stochastic estimator for the trace of the inverse of a large, sparse matrix A. The variance of the estimator is the sum of the squares of the off-diagonal elements of A -1 . Therefore, this technique computes probing vectors that when used in the estimator annihilate the largest off-diagonal elements. For matrices that display decay of the magnitude of |A$^{-1}_{ij}$| with the graph distance between nodes i and j, this is achieved through graph coloring of increasing powers A k . Equivalently, when a matrix stems from a lattice discretization, it is computationally beneficial to find a distance-k coloring of the lattice. Previously, a hierarchical coloring was proposed so that k can be increased at runtime as needed without discarding previous work. In this work, we study probing for the more general problem of computing the trace of a permutation of A -1 , say PA -1 . The motivation comes from lattice quantum chromodynamics (QCD), where we need to construct “disconnected diagrams” to extract flavor-separated generalized parton functions. In lattice QCD, where the matrix has a four-dimensional toroidal lattice structure, these nonlocal operators correspond to a PA -1 , where P is the permutation relating to some displacement $\vec{p}$ in one or more dimensions. We focus on a single dimension displacement (p), but our methods are general. We show that probing on A k or (PA) k does not annihilate the largest magnitude elements. To resolve this issue, our displacement-based probing works on PA k using a new coloring scheme that works directly on appropriately displaced neighborhoods on the lattice. We prove lower bounds on the number of colors needed and study the effect of this scheme on variance reduction, both theoretically and experimentally on a real-world lattice QCD calculation. We achieve orders of magnitude speedup over the unprobed or the naively probed methods.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2007

Predicting Rocket or Jet Noise in Real Time

A semi-empirical theoretical model and a C++ computer program that implements the model have been developed for use in predicting the noise generated by a rocket or jet engine. The computer program, entitled the Realtime Rocket and Jet Engine Noise Analysis and Prediction Software, is one of two main subsystems of the Acoustic Prediction/Measurement Tool, which comprises software, acoustic instrumentation, and electronic hardware combined to afford integrated capabilities for real-time prediction and measurement of noise emitted by rocket and jet engines. [The other main subsystem, consisting largely of acoustic instrumentation and electronic hardware, is described in Wireless Acoustic Measurement System, which appears elsewhere in this section.] The theoretical model was derived from the fundamental laws of fluid mechanics, as first was done by M. J. Lighthill in his now famous theory of aerodynamically generated sound. The far-field approximation of the Lighthill theory is incorporated into this model. Many other contributions from various researchers have also been introduced into the model. The model accounts for two noise components: shear noise and self noise. The final result of the model is expressed in terms of a volume integral of the acoustic intensities attributable to these two components, subject to various directivity coefficients. The computer program was written to solve the volume integral. The inputs required by the program are two data files from a computational fluid dynamics (CFD) simulation of the flow of interest: the computational-grid file and the solution file. The CFD solution should be one that has been obtained for conditions that closely approximate those of an experimental test that is yet to be performed. In the current state of development of the model and software, it is recommended that the observation points lie along a radius at an angle >60 from the jet axis. The software provides, and is driven via, a graphical user interface, which facilitates its use. Optionally, the program accepts additional input in the form of data on the measured sound pressure level as a function of frequency at a given far-field location, preferably at an angle of 90 from the jet axis. The user is prompted to use default empirical constants or to choose constants based the measurement data. The user can view the results and compare them with other computational or experimental data. Once satisfied with the results, the user can save a graph of the results in a file that can be imported into documents.

Frendi, Kader↗

NASA NTRS2013

Scheduling Operations for Massive Heterogeneous Clusters

High-performance computing (HPC) programming has become increasingly difficult with the advent of hybrid supercomputers consisting of multicore CPUs and accelerator boards such as the GPU. Manual tuning of software to achieve high performance on this type of machine has been performed by programmers. This is needlessly difficult and prone to being invalidated by new hardware, new software, or changes in the underlying code. A system was developed for task-based representation of programs, which when coupled with a scheduler and runtime system, allows for many benefits, including higher performance and utilization of computational resources, easier programming and porting, and adaptations of code during runtime. The system consists of a method of representing computer algorithms as a series of data-dependent tasks. The series forms a graph, which can be scheduled for execution on many nodes of a supercomputer efficiently by a computer algorithm. The schedule is executed by a dispatch component, which is tailored to understand all of the hardware types that may be available within the system. The scheduler is informed by a cluster mapping tool, which generates a topology of available resources and their strengths and communication costs. Software is decoupled from its hardware, which aids in porting to future architectures. A computer algorithm schedules all operations, which for systems of high complexity (i.e., most NASA codes), cannot be performed optimally by a human. The system aids in reducing repetitive code, such as communication code, and aids in the reduction of redundant code across projects. It adds new features to code automatically, such as recovering from a lost node or the ability to modify the code while running. In this project, the innovators at the time of this reporting intend to develop two distinct technologies that build upon each other and both of which serve as building blocks for more efficient HPC usage. First is the scheduling and dynamic execution framework, and the second is scalable linear algebra libraries that are built directly on the former.

Humphrey, John↗