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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Efficient numerical methods to solve sparse linear equations with application to PageRank

Over the last two decades, the PageRank problem has received increased interest from the academic community as an efficient tool to estimate web-page importance in information retrieval. Despite numerous developments, the design of efficient optimization algorithms for the PageRank problem is still a challenge. Here, we propose three new algorithms with a linear time complexity for solving the problem over a bounded-degree graph. The idea behind them is to set up the PageRank as a convex minimization problem over a unit simplex, and then solve it using iterative methods with small iteration complexity. Our theoretical results are supported by an extensive empirical justification using real-world and simulated data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Final Technical Report on Quantifying Dependability Attributes of Software Based Safety Critical Instrumentation and Control Systems in Nuclear Power Plants

With the current transition from analog to digital instrumentation and control systems in nuclear power plants, the number and variety of software-based systems have significantly increased. The sophisticated nature and increasing complexity of software raises trust in these systems as a significant challenge. The trust placed in a software system is typically termed software dependability. Software dependability analysis faces uncommon challenges since software systems’ characteristics differ from those of hardware systems. The lack of systematic science-based methods for quantifying the dependability attributes in software-based instrumentation as well as control systems in safety critical applications has proved itself to be a significant inhibitor to the expanded use of modern digital technology in the nuclear industry. Dependability refers to the ability of a system to deliver a service that can be trusted. Dependability is commonly considered as a general concept that encompasses different attributes, e.g., reliability, safety, security, availability and maintainability. Dependability research has progressed significantly over the last few decades. For example, various assessment models and/or design approaches have been proposed for software reliability, software availability and software maintainability. Advances have also been made to integrate multiple dependability attributes, e.g., integrating security with other dependability attributes, measuring availability and maintainability, modeling reliability and availability, quantifying reliability and security, exploring the dependencies between security and safety and developing integrated analysis models. However, there is still a lack of understanding of the dependencies between various dependability attributes as a whole and of how such dependencies are formed. To address the need for quantification and give a more objective basis to the review process -- therefore reducing regulatory uncertainty -- measures and methods are needed to assess dependability attributes early on, as well as throughout the life-cycle process of software development. In this research, extensive expert opinion elicitation is used to identify the measures and methods for assessing software dependability. Semi-structured questionnaires were designed to elicit expert knowledge. A new notation system, Causal Mechanism Graphing, was developed to extract and represent such knowledge. The Causal Mechanism Graphs were merged, thus, obtaining the consensus knowledge shared by the domain experts. In this report, we focus on how software contributes to dependability. However, software dependability is not discussed separately from the context of systems or socio-technical systems. Specifically, this report focuses on software dependability, reliability, safety, security, availability, and maintainability. Our research was conducted in the sequence of stages found below. Each stage is further examined in its corresponding chapter. Stage 1 (Chapter 2): Elicitation of causal maps describing the dependencies between dependability attributes. These causal maps were constructed using expert opinion elicitation. This chapter describes the expert opinion elicitation process, the questionnaire design, the causal map construction method and the causal maps obtained. Stage 2 (Chapter 3): Elicitation of the causal map describing the occurrence of the event of interest for each dependability attribute. The causal mechanisms for the “event of interest” were extracted for each of the software dependability attributes. The “event of interest” for a dependability attribute is generally considered to be the “attribute failure”, e.g. security failure. The extraction was based on the analysis of expert elicitation results obtained in Stage 1. Stage 3 (Chapter 4): Identification of relevant measurements. Measures for the “events of interest” and their causal mechanisms were obtained from expert opinion elicitation for each of the software dependability attributes. The measures extracted are presented in this chapter. Stage 4 (Chapter 5): Assessment of the coverage of the causal maps via measures. Coverage was assessed to determine whether the measures obtained were sufficient to quantify software dependability, and what measures are further required. Stage 5 (Chapter 6): Identification of “missing” measures and measurement approaches for concepts not covered. New measures, for concepts that had not been covered sufficiently as determined in Stage 4, were identified using supplementary expert opinion elicitation as well as literature reviews. Stage 6 (Chapter 7): Building of a detailed quantification model based on the causal maps and measurements obtained. Ability to derive such a quantification model shows that the causal models and measurements derived from the previous stages (Stage 1 to Stage 5) can form the technical basis for developing dependability quantification models. Scope restrictions have led us to prioritize this demonstration effort. The demonstration was focused on a critical system, i.e. the reactor protection system. For this system, a ranking of the software dependability attributes by nuclear stakeholders was developed. As expected for this application, the stakeholder ranking identified safety as the most critical attribute to be quantified. A safety quantification model limited to the requirements phase of development was built. Two case studies were conducted for verification. A preliminary control gate for software safety for the requirements stage was proposed and applied to the first case study. The control gate allows a cost effective selection of the duration of the requirements phase.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Application of Modified Meshgraphnets for Subsurface Prediction during CO2 Sequestration

In the face of the increasingly dire consequences of anthropogenic climate change, capturing and storing carbon dioxide is paramount. However, several impediments exist to the safe and effective subsurface storage of CO2, such as cost of transport, identification of suitable sites for subsurface storage, and assessment of long-term risk from storage in subsurface aquifers. Accurate subsurface modeling is necessary to ensure that CO2 storage is both safe and effective. Still, such modeling has traditionally required either substantial time and computational power (numerical simulation) or a substantial amount of pre-existing data for training (machine learning models). Additionally, these models lack flexibility in dealing with both changes in discretization of the input data and generalizability beyond the data on which they are trained. In order to address these issues, this research applies graph neural networks (GNNs) to predict subsurface saturation and pressure during CO₂ injection in a model of the Illinois Basin-Decatur Project (IBDP). GNNs provide a flexible, intuitive method for representing and manipulating complex unstructured data, which is often found in many practical domain problems such as fluid flow and subsurface characterization. These unstructured grids are easily represented in GNNs by representing spatially-localized features such as permeability, porosity, saturation, and pressure as nodes in a graph and relationships between these properties as edges connecting these nodes. This research applies a specific GNN model called MeshGraphNets (MGN) to model the change in CO2 saturation and pressure over a 50-month time period (36 months of injection, 14 months post-injection). The MGN model leverages a message passing process that allows the network to learn both the spatial and temporal dynamics of this system simultaneously. Additionally, training on a limited dataset (64 realizations, 20 time points each) resulted in a high degree of accuracy in saturation prediction both within the same timeframe as the training (20 months, 0.039 average RMSE) and when projecting out to the end of injection (36 months, 0.053 average RMSE). Temporal predictions such as those generated by MGNs and other similar models are prone to accumulated error over time; in order to address this, a multi-step rollout (MSR) training process was applied to calculate training loss. This method mimics the forward prediction during inference by “rolling out” multiple time points in a single training step using the previous prediction as input to the MGN model. By calculating the loss several time steps forward from the current prediction, the model is forced to find a more stable state over time. Application of MSR to the MGN model resulted in an average 15% reduction in inference error over time during forward prediction. This study showcases the immense potential of GNNs as a game-changing methodology for predicting pressure and saturation evolution in CCS projects, ultimately paving the way for more sustainable and effective carbon storage solutions. Presentation prepared for the 2024 AiChE Annual Meeting, October 27 to November 1 2024, San Diego, CA.

Holcomb, Paul↗
NASA NTRS1955

Calculations of Laminar Heat Transfer Around Cylinders of Arbitrary Cross Section and Transpiration-Cooled Walls with Application to Turbine Blade Cooling

An approximate method for the development of flow and thermal boundary layers in the laminar region on cylinders with arbitrary cross section and transpiration-cooled walls is obtained by the use of Karman's integrated momentum equation and an analogous heat-flow equation. Incompressible flow with constant property values throughout the boundary layer is assumed. The velocity and temperature profiles within the boundary layer are approximated by expressions composed of trigonometric functions. Shape parameters for these profiles and functions necessary for the solution of the boundary-layer equations are presented as graphs so that the calculation for any specific case is reduced to the solution of two first-order differential equations. This method is applied to determine local heat-transfer coefficients and surface temperatures in the laminar flow region of the transpiration-cooled turbine blades for a given coolant flow rate, or to calculate the coolant flow distribution which is necessary in order to keep the blade temperature uniform along the surface.

Eckert, E R G↗
NASA NTRS1991

A nonrecursive 'Order N' preconditioned conjugate gradient/range space formulation of MDOF dynamics

This paper addresses the requirements of present-day mechanical system simulations of algorithms that induce parallelism on a fine scale and of transient simulation methods which must be automatically load balancing for a wide collection of system topologies and hardware configurations. To this end, a combination range space/preconditioned conjugage gradient formulation of multidegree-of-freedon dynamics is developed, which, by employing regular ordering of the system connectivity graph, makes it possible to derive an extremely efficient preconditioner from the range space metric (as opposed to the system coefficient matrix). Because of the effectiveness of the preconditioner, the method can achieve performance rates that depend linearly on the number of substructures. The method, termed 'Order N' does not require the assembly of system mass or stiffness matrices, and is therefore amenable to implementation on work stations. Using this method, a 13-substructure model of the Space Station was constructed.

Kurdila, A. J.↗
DOE OSTI2017

Eigenvector centrality for geometric and topological characterization of porous media

Solving flow and transport through complex geometries such as porous media is computationally difficult. Such calculations usually involve the solution of a system of discretized differential equations, which could lead to extreme computational cost depending on the size of the domain and the accuracy of the model. Geometric simplifications like pore-networks, where the pores are represented by nodes and pore throats by edges connecting pores, have been proposed. These models, despite their ability to preserve the connectivity of the medium, have difficulties in capturing preferential paths (high velocity) and stagnation zones (low velocity) as they do not consider the specific relations between nodes. Nonetheless, network theory approaches, where a complex network is a graph, can help to simplify and better understand fluid dynamics and transport in porous media. Here we present a novel method to address these issues based on eigenvector centrality, which has been corrected to overcome the centralization problem, and modified to introduce a bias in the centrality distribution along a particular direction to address the flow and transport anisotropy in porous media. We compare the model predictions with millifluidic transport experiments, which shows that, albeit simple, this technique is computationally efficient and has potential for predicting preferential paths and stagnation zones for flow and transport in porous media. We propose to use eigenvector centrality probability distribution to compute entropy as an indicator of the ‘mixing capacity’ of the system.

58 GEOSCIENCES↗
DOE OSTI2023

Scalable generalized screening for high-order terms in the many-body expansion: Algorithm, open-source implementation, and demonstration

The many-body expansion lies at the heart of numerous fragment-based methods that are intended to sidestep the nonlinear scaling of ab initio quantum chemistry, making electronic structure calculations feasible in large systems. In principle, inclusion of higher-order n-body terms ought to improve the accuracy in a controllable way, but unfavorable combinatorics often defeats this in practice and applications with n ≥ 4 are rare. Here, we outline an algorithm to overcome this combinatorial bottleneck, based on a bottom-up approach to energy-based screening. This is implemented within a new open-source software application (“Fragme∩t”), which is integrated with a lightweight semi-empirical method that is used to cull subsystems, attenuating the combinatorial growth of higher-order terms in the graph that is used to manage the calculations. This facilitates applications of unprecedented size, and we report four-body calculations in (H2O)64 clusters that afford relative energies within 0.1 kcal/mol/monomer of the supersystem result using less than 10% of the unique subsystems. We also report n-body calculations in (H2O)20 clusters up to n = 8, at which point the expansion terminates naturally due to screening. These are the largest n-body calculations reported to date using ab initio electronic structure theory, and they confirm that high-order n-body terms are mostly artifacts of basis-set superposition error.

Chemistry↗
DOE OSTI2015

A NOVEL TECHNIQUE TO IMPROVE PHOTOMETRY IN CONFUSED IMAGES USING GRAPHS AND BAYESIAN PRIORS

We present a new technique for overcoming confusion noise in deep far-infrared Herschel space telescope images making use of prior information from shorter λ < 2 μm wavelengths. For the deepest images obtained by Herschel, the flux limit due to source confusion is about a factor of three brighter than the flux limit due to instrumental noise and (smooth) sky background. We have investigated the possibility of de-confusing simulated Herschel PACS 160 μm images by using strong Bayesian priors on the positions and weak priors on the flux of sources. We find the blended sources and group them together and simultaneously fit their fluxes. We derive the posterior probability distribution function of fluxes subject to these priors through Monte Carlo Markov Chain (MCMC) sampling by fitting the image. Assuming we can predict the FIR flux of sources based on the ultraviolet-optical part of their SEDs to within an order of magnitude, the simulations show that we can obtain reliable fluxes and uncertainties at least a factor of three fainter than the confusion noise limit of 3σ {sub c} = 2.7 mJy in our simulated PACS-160 image. This technique could in principle be used to mitigate the effects of source confusion in any situation where one has prior information of positions and plausible fluxes of blended sources. For Herschel, application of this technique will improve our ability to constrain the dust content in normal galaxies at high redshift.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

A Confidence-Guided Technique for Tracking Time-Varying Features

Application scientists often employ feature tracking algorithms to capture the temporal evolution of various features in their simulation data. However, as the complexity of the scientific features is increasing with the advanced simulation modeling techniques, quantification of reliability of the feature tracking algorithms is becoming important. One of the desired requirements for any robust feature tracking algorithm is to estimate its confidence during each tracking step so that the results obtained can be interpreted without any ambiguity. To address this, we develop a confidence-guided feature tracking algorithm that allows reliable tracking of user-selected features and presents the tracking dynamics using a graph-based visualization along with the spatial visualization of the tracked feature. Here, the efficacy of the proposed method is demonstrated by applying it to two scientific datasets containing different types of time-varying features.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

Supercomputing of supersonic flows using upwind relaxation and MacCormack schemes

The performance of two numerical solution schemes, (1) an implicit upwind relaxation with a finite-volume discretization (Thomas and Walters, 1985) and (2) an explicit-implicit MacCormack (1981) scheme with a finite-difference discretization, is compared in two-dimensional simulations of supersonic flow past a flat plate with leading edge, a rearward-facing step, a 10-deg compression corner, a NACA 0012 airfoil at high angle of attack, and a cavity. The algebraic turbulence model, the solution methods, and the boundary conditions and SIMD coding are explained, and the results are presented in tables and graphs and characterized with reference to published experimental data. Scheme (1) is found to converge more rapidly and to give more accurate results than (2) in a wide range of problem types.

Baysal, O.↗
NASA NTRS1988

Full configuration-interaction benchmark calculations for AlH

Full CI and CASSCF/SOCI theoretical computations are presented for the X 1Sigma(+), A 1Pi, and C 1Sigma(+) states of AlH. The aim is to establish benchmark data to calibrate methods which describe valence-Rydberg transitions in other molecules. The results are presented in extensive tables and graphs and compared with published theoretical and experimental values, and the conditions under which CASSCF/SOCI calculations accurately reproduce the FCI results are defined.

Bauschlicher, Charles W., Jr.↗
DOE OSTI2016

WE-AB-209-09: Optimization of Rotational Arc Station Parameter Optimized Radiation Therapy

Purpose: To develop a fast optimization method for station parameter optimized radiation therapy (SPORT) and show that SPORT is capable of improving VMAT in both plan quality and delivery efficiency. Methods: The angular space from 0° to 360° was divided into 180 station points (SPs). A candidate aperture was assigned to each of the SPs based on the calculation results using a column generation algorithm. The weights of the apertures were then obtained by optimizing the objective function using a state-of-the-art GPU based Proximal Operator Graph Solver (POGS) within seconds. Apertures with zero or low weight were thrown out. To avoid being trapped in a local minimum, a stochastic gradient descent method was employed which also greatly increased the convergence rate of the objective function. The above procedure repeated until the plan could not be improved any further. A weighting factor associated with the total plan MU also indirectly controlled the complexities of aperture shapes. The number of apertures for VMAT and SPORT was confined to 180. The SPORT allowed the coexistence of multiple apertures in a single SP. The optimization technique was assessed by using three clinical cases (prostate, H&N and brain). Results: Marked dosimetric quality improvement was demonstrated in the SPORT plans for all three studied cases. Prostate case: the volume of the 50% prescription dose was decreased by 22% for the rectum. H&N case: SPORT improved the mean dose for the left and right parotids by 15% each. Brain case: the doses to the eyes, chiasm and inner ears were all improved. SPORT shortened the treatment time by ∼1 min for the prostate case, ∼0.5 min for brain case, and ∼0.2 min for the H&N case. Conclusion: The superior dosimetric quality and delivery efficiency presented here indicates that SPORT is an intriguing alternative treatment modality.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Learning Optimal Multigrid Smoothers via Neural Networks

Multigrid methods are one of the most efficient techniques for solving large sparse linear systems arising from partial differential equations (PDEs) and graph Laplacians from machine learning applications. One of the key components of multigrid is smoothing, which aims at reducing high-frequency errors on each grid level. However, finding optimal smoothing algorithms is problem-dependent and can impose challenges for many problems. In this paper, we propose an efficient adaptive framework for learning optimized smoothers from operator stencils in the form of convolutional neural networks (CNNs). Here, the CNNs are trained on small-scale problems from a given type of PDEs based on a supervised loss function derived from multigrid convergence theories and can be applied to large-scale problems of the same class of PDEs. Numerical results on anisotropic rotated Laplacian problems and variable coefficient diffusion problems demonstrate improved convergence rates and solution time compared with classical hand-crafted relaxation methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

EnsembleGraph: Interactive Visual Analysis of Spatial-Temporal Behavior for Ensemble Simulation Data

We present a novel visualization framework—EnsembleGraph— for analyzing ensemble simulation data, in order to help scientists understand behavior similarities between ensemble members over space and time. A graph-based representation is used to visualize individual spatiotemporal regions with similar behaviors, which are extracted by hierarchical clustering algorithms. A user interface with multiple-linked views is provided, which enables users to explore, locate, and compare regions that have similar behaviors between and then users can investigate and analyze the selected regions in detail. The driving application of this paper is the studies on regional emission influences over tropospheric ozone, which is based on ensemble simulations conducted with different anthropogenic emission absences using the MOZART-4 (model of ozone and related tracers, version 4) model. We demonstrate the effectiveness of our method by visualizing the MOZART-4 ensemble simulation data and evaluating the relative regional emission influences on tropospheric ozone concentrations. Positive feedbacks from domain experts and two case studies prove efficiency of our method.

ensemble simulation↗
DOE OSTI2020

Online Event Detection in Synchrophasor Data with Graph Signal Processing

Online detection of anomalies is crucial to enhancing the reliability and resiliency of power systems. We propose a novel data-driven online event detection algorithm with synchrophasor data using graph signal processing. In addition to being extremely scalable, our proposed algorithm can accurately capture and leverage the spatio-temporal correlations of the streaming PMU data. This paper also develops a general technique to decouple spatial and temporal correlations in multiple time series. Finally, we develop a unique framework to construct a weighted adjacency matrix and graph Laplacian for product graph. Case studies with real-world, large-scale synchrophasor data demonstrate the scalability and accuracy of our proposed event detection algorithm. Compared to the state-of-the-art benchmark, the proposed method not only achieves higher detection accuracy but also yields higher computational efficiency.

Event detection↗
DOE OSTI2024

Introducing Molecular Hypernetworks for Discovery in Multidimensional Metabolomics Data

Orthogonal separations of data from high-resolution mass spectrometry can provide insight into sample composition and address challenges of complete annotation of molecules in untargeted metabolomics. “Molecular networks” (MNs), as used in the Global Natural Products Social Molecular Networking platform, are a prominent strategy for exploring and visualizing molecular relationships and improving annotation. MNs are mathematical graphs showing the relationships between measured multidimensional data features. MNs also show promise for using network science algorithms to automatically identify targets for annotation candidates and to dereplicate features associated with a single molecular identity. Here, this paper introduces “molecular hypernetworks” (MHNs) as more complex MN models able to natively represent multiway relationships among observations. Compared to MNs, MHNs can more parsimoniously represent the inherent complexity present among groups of observations, initially supporting improved exploratory data analysis and visualization. MHNs also promise to increase confidence in annotation propagation, for both human and analytical processing. We first illustrate MHNs with simple examples, and build them from liquid chromatography- and ion mobility spectrometry-separated MS data. We then describe a method to construct MHNs directly from existing MNs as their “clique reconstructions”, demonstrating their utility by comparing examples of previously published graph-based MNs to their respective MHNs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Orbital Conflict: Cutting Planes for Symmetric Integer Programs

Cutting planes have been an important factor in the impressive progress made by integer programming (IP) solvers in the past two decades. However, cutting planes have had little impact on improving performance for symmetric IPs. Rather, the main breakthroughs for solving symmetric IPs have been achieved by cleverly exploiting symmetry in the enumeration phase of branch and bound. In this work, we introduce a hierarchy of cutting planes that arise from a reinterpretation of symmetry-exploiting branching methods. There are too many inequalities in the hierarchy to be used efficiently in a direct manner. However, the lowest levels of this cutting-plane hierarchy can be implicitly exploited by enhancing the conflict graph of the integer programming instance and by generating inequalities such as clique cuts valid for the stable set relaxation of the instance. We provide computational evidence that the resulting symmetry-powered clique cuts can improve state-of-the-art symmetry-exploiting methods. Furthermore, the inequalities are then employed in a two-phase approach with high-throughput computations to solve heretofore unsolved symmetric integer programs arising from covering designs, establishing for the first time the covering radii of two binary-ternary codes.

97 MATHEMATICS AND COMPUTING↗