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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Sensitivity analysis in multipole-accelerated panel methods for potential flow

In the design of an airframe, the effect of changing the geometry on resulting computations is necessary for design optimization. The geometry is defined in terms of a series of design variables, including design variables to define the wing planform, tail, canard, pylon, and nacelle. Design optimization in this research is based on how these design variable affect the potential flow. The potential flow is computed as a function of the geometry and location of a series of panels describing the airframe, which are in turn a function of the design variables. Multipole accelerated panel methods improve the computational complexity of the problem and thus are an attractive approach. To utilize the methods in design optimization, it was necessary to define the appropriate sensitivity derivatives. The overhead incurred from finding the sensitivity derivatives in conjunction with the original computation should be small. This research developed the background for multipole-accelerated panel methods and the framework for finding sensitivity derivatives in the methods. Potential flow panel codes are commonly used for powered-lift aerodynamic predictions for three dimensional geometries. Given an airframe which has been discretized into a series of panels to define the airframe geometry, potential is computed as a function of the influence of all panels on all other panels. This is a computationally intensive problem for which efficient solutions are desired to improve the computational time and to allow greater resolution by use of more panels. One such solution is the use of hierarchical multipole methods which entail approximations of the effects of far-field terms. Hierarchical multipole methods have become prevalent in molecular dynamics and gravitational physics, and have been introduced into the fields of capacitance calculations, computational fluid dynamics, and electromagnetics. The methods utilize multipole expansions to describe the effect of bodies (i.e. particles, astrophysical bodies, panels, etc.) within a sphere on points distant from the sphere, where the influence diminishes as a function of distance. The expansions are exact with infinite series, however, for practical computations, the series are truncated and accuracy is selected based on the number of terms retained in the expansions. A hierarchical tree structure groups bodies together based on proximity to allow definition of multipole expansions for each group. The multipole expansions are then used to compute the effect of the bodies in a group on distant bodies.

Leathrum, James F., Jr.↗
NASA NTRS1994

On the application of under-decimated filter banks

Maximally decimated filter banks have been extensively studied in the past. A filter bank is said to be under-decimated if the number of channels is more than the decimation ratio in the subbands. A maximally decimated filter bank is well known for its application in subband coding. Another application of maximally decimated filter banks is in block filtering. Convolution through block filtering has the advantages that parallelism is increased and data are processed at a lower rate. However, the computational complexity is comparable to that of direct convolution. More recently, another type of filter bank convolver has been developed. In this scheme, the convolution is performed in the subbands. Quantization and bit allocation of subband signals are based on signal variance, as in subband coding. Consequently, for a fixed rate, the result of convolution is more accurate than is direct convolution. This type of filter bank convolver also enjoys the advantages of block filtering, parallelism, and a lower working rate. Nevertheless, like block filtering, there is no computational saving. In this article, under-decimated systems are introduced to solve the problem. The new system is decimated only by half the number of channels. Two types of filter banks can be used in the under-decimated system: the discrete Fourier transform (DFT) filter banks and the cosine modulated filter banks. They are well known for their low complexity. In both cases, the system is approximately alias free, and the overall response is equivalent to a tunable multilevel filter. Properties of the DFT filter banks and the cosine modulated filter banks can be exploited to simultaneously achieve parallelism, computational saving, and a lower working rate. Furthermore, for both systems, the implementation cost of the analysis or synthesis bank is comparable to that of one prototype filter plus some low-complexity modulation matrices. The individual analysis and synthesis filters have complex coefficients in the DFT filter banks but have real coefficients in the cosine modulated filter banks.

Lin, Y.-P.↗
DOE OSTI2022

The Effect of Geometry, Spin, and Orbital Optimization in Achieving Accurate, Correlated Results for Iron–Sulfur Cubanes

Iron–sulfur clusters comprise an important functional motif in the catalytic centers of biological systems, capable of enabling important chemical transformations at ambient conditions. This remarkable capability derives from a notoriously complex electronic structure that is characterized by a high density of states that is sensitive to geometric changes. The spectral sensitivity to subtle geometric changes has received little attention from correlated, large active space calculations, owing partly to the exceptional computational complexity for treating these large and correlated systems accurately. Here, to provide insight into this aspect, we report the first Complete Active Space Self Consistent Field (CASSCF) calculations for different geometries of the [Fe(II/III) 4 S 4 (SMe) 4 ] -2 clusters using two complementary, correlated solvers: spin-pure Adaptive Sampling Configuration Interaction (ASCI) and Density Matrix Renormalization Group (DMRG). We find that the previously established picture of a double-exchange driven magnetic structure, with minute energy gaps (<1 mHa) between consecutive spin states, has a weak dependence on the underlying geometry. However, the spin gap between the singlet and the spin state 2S + 1 = 19, corresponding to a maximal number of Fe-d electrons being unpaired and of parallel spin, is strongly geometry dependent, changing by a factor of 3 upon slight deformations that are still within biologically relevant parameters. The CASSCF orbital optimization procedure, using active spaces as large as 86 electrons in 52 orbitals, was found to reduce this gap compared to typical mean-field orbital approaches. Our results show the need for performing large active space calculations to unveil the challenging electronic structure of these complex catalytic centers and should serve as accurate starting points for fully correlated treatments upon inclusion of dynamical correlation outside the active space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1994

AutoClass: A Bayesian Approach to Classification

We describe a Bayesian approach to the untutored discovery of classes in a set of cases, sometimes called finite mixture separation or clustering. The main difference between clustering and our approach is that we search for the "best" set of class descriptions rather than grouping the cases themselves. We describe our classes in terms of a probability distribution or density function, and the locally maximal posterior probability valued function parameters. We rate our classifications with an approximate joint probability of the data and functional form, marginalizing over the parameters. Approximation is necessitated by the computational complexity of the joint probability. Thus, we marginalize w.r.t. local maxima in the parameter space. We discuss the rationale behind our approach to classification. We give the mathematical development for the basic mixture model and describe the approximations needed for computational tractability. We instantiate the basic model with the discrete Dirichlet distribution and multivariant Gaussian density likelihoods. Then we show some results for both constructed and actual data.

Stutz, John↗
DOE OSTI2018

GPU Data Access on Complex Geometries for D3Q19 Lattice Boltzmann Method

GPU performance of the lattice Boltzmann method (LBM) depends heavily on memory access patterns. When LBM is advanced with GPUs on complex computational domains, geometric data is typically accessed indirectly, and lattice data is typically accessed lexicographically in the Structure of Array (SoA) layout. Although there are a variety of existing access patterns beyond the typical choices, no study has yet examined the relative efficacy between them. Here, we compare a suite of memory access schemes via empirical testing and performance modeling. We find strong evidence that semi-direct addressing is the superior addressing scheme for the majority of cases examined: Semi-direct addressing increases computational speed and often reduces memory consumption. For lattice layout, we find that the Collected Structure of Arrays (CSoA) layout outperforms the SoA layout. When compared to state-of-the-art practices, our recommended addressing modifications lead to performance gains between 10-40% across different complex geometries, fluid volume fractions, and resolutions. The modifications also lead to a decrease in memory consumption by as much as 17%. Having discovered these improvements, we examine a highly resolved arterial geometry on a leadership class system. On this system we present the first near-optimal strong results for LBM with arterial geometries run on GPUs. We also demonstrate that the above recommendations remain valid for large scale, many device simulations, which leads to an increased computational speed and average memory usage reductions. To understand these observations, we employ performance modeling which reveals that semi-direct methods outperform indirect methods due to a reduced number of total loads/stores in memory, and that CSoA outperforms SoA and bundling due to improved caching behavior.

Herschlag, Gregory↗
DOE OSTI2021

Spectral Equivalence of Low-Order Discretizations for High-Order H(curl) and H(div) Spaces

In this paper, we present spectral equivalence results for high-order tensor product edge- and face-based finite elements for the H(curl) and H(div) function spaces. Specifically, we show for certain choices of shape functions that the mass and stiffness matrices of the high-order elements are spectrally equivalent to those for an assembly of low-order elements on the associated Gauss--Lobatto--Legendre mesh. Based on this equivalence, efficient preconditioners can be designed with favorable computational complexity. Numerical results are presented which confirm the theory and demonstrate the benefits of the equivalence results for overlapping Schwarz preconditioners.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Spectral Equivalence Properties of Higher-Order Tensor Product Finite Elements and Applications to Preconditioning

In this study, we present spectral equivalence results for higher-order tensor product edge-, face- and interior-based finite elements. Specifically, we show for certain choices of shape functions that the mass and stiffness matrices of the higher-order elements are spectrally equivalent to those for an assembly of lowest-order elements on the associated Gauss-Lobatto-Legendre mesh. Based on this equivalence, efficient preconditioners can be designed with favorable computational complexity. Numerical results are presented which confirm the theory and demonstrate the benefits of the equivalence results for overlapping Schwarz preconditioners.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Efficient Monte Carlo event generation for neutrino-nucleus exclusive cross sections

Modern neutrino-nucleus cross section computations need to incorporate sophisticated nuclear models to achieve greater predictive precision. However, the computational complexity of these advanced models often limits their practicality for experimental analyses. To address this challenge, we introduce a new Monte Carlo method utilizing normalizing flows to generate surrogate cross sections that closely approximate those of the original model while significantly reducing computational overhead. As a case study, we built a Monte Carlo event generator for the neutrino-nucleus cross section model developed by the Ghent group. This model employs a Hartree-Fock procedure to establish a quantum mechanical framework in which both the bound and scattering nucleon states are solutions to the mean-field nuclear potential. The surrogate cross sections generated by our method demonstrate excellent accuracy with a relative effective sample size of more than 98.4%, providing a computationally efficient alternative to traditional Monte Carlo sampling methods for differential cross sections.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1988

Mentat: An object-oriented macro data flow system

Mentat, an object-oriented macro data flow system designed to facilitate parallelism in distributed systems, is presented. The macro data flow model is a model of computation similar to the data flow model with two principal differences: the computational complexity of the actors is much greater than in traditional data flow systems, and there are persistent actors that maintain state information between executions. Mentat is a system that combines the object-oriented programming paradigm and the macro data flow model of computation. Mentat programs use a dynamic structure called a future list to represent the future of computations.

Grimshaw, Andrew S.↗
NASA NTRS2000

On-Line, Self-Learning, Predictive Tool for Determining Payload Thermal Response

This paper will present the results of a joint ManTech / Goddard R&D effort, currently under way, to develop and test a computer based, on-line, predictive simulation model for use by facility operators to predict the thermal response of a payload during thermal vacuum testing. Thermal response was identified as an area that could benefit from the algorithms developed by Dr. Jeri for complex computer simulations. Most thermal vacuum test setups are unique since no two payloads have the same thermal properties. This requires that the operators depend on their past experiences to conduct the test which requires time for them to learn how the payload responds while at the same time limiting any risk of exceeding hot or cold temperature limits. The predictive tool being developed is intended to be used with the new Thermal Vacuum Data System (TVDS) developed at Goddard for the Thermal Vacuum Test Operations group. This model can learn the thermal response of the payload by reading a few data points from the TVDS, accepting the payload's current temperature as the initial condition for prediction. The model can then be used as a predictive tool to estimate the future payload temperatures according to a predetermined shroud temperature profile. If the error of prediction is too big, the model can be asked to re-learn the new situation on-line in real-time and give a new prediction. Based on some preliminary tests, we feel this predictive model can forecast the payload temperature of the entire test cycle within 5 degrees Celsius after it has learned 3 times during the beginning of the test. The tool will allow the operator to play "what-if' experiments to decide what is his best shroud temperature set-point control strategy. This tool will save money by minimizing guess work and optimizing transitions as well as making the testing process safer and easier to conduct.

Jen, Chian-Li↗
NASA NTRS2018

Digital Technologies at NASA for Science and Engineering

While scientific and engineering advancements used to rely primarily on theoretical studies and physical experiments, today digital technology enabled by petaflops-scale supercomputers is an equal, if not a greater, contributor to such achievements. In addition, computational modeling and simulation serves as a predictive tool that is not otherwise available. As a result, the use of high performance computing is integral to NASA's work in all mission areas such as space exploration, aeronautics, and scientific discovery. But traditional supercomputing alone is not sufficient for all of the space agency's needs. The success of many NASA missions depends on solving complex computing challenges, some of which are NP-hard (decision theory) if using classical solution methods. Quantum computing promises an unprecedented ability to solve such intractable problems by harnessing quantum mechanical effects such as tunneling, superposition, and entanglement. Another disruptive digital technology is neuromorphic computing that uses brain-inspired lessons to generate new architectures that are much more energy efficient, and capable of massive parallel processing and learning in-situ. Finally, with large amounts of observational and computational data sets, the opportunities of big data and data analytics can be leveraged to enable deep learning and knowledge discovery - it's all a massive digital transformation. This talk will be an overview how NASA utilizes digital technologies for its science and engineering efforts.

Biswas, Rupak↗
DOE OSTI2020

Material coherence from trajectories via Burau eigenanalysis of braids

In this paper, we provide a numerical tool to study a material’s coherence from a set of 2D Lagrangian trajectories sampling a dynamical system, i.e., from the motion of passive tracers. We show that eigenvectors of the Burau representation of a topological braid derived from the trajectories have levelsets corresponding to components of the Nielsen–Thurston decomposition of the dynamical system. One can thus detect and identify clusters of space–time trajectories corresponding to coherent regions of the dynamical system by solving an eigenvalue problem. Unlike previous methods, the scalable computational complexity of our braid-based approach allows the analysis of large amounts of trajectories.

36 MATERIALS SCIENCE↗
NASA NTRS1986

Dynamic remapping of parallel computations with varying resource demands

A large class of computational problems is characterized by frequent synchronization, and computational requirements which change as a function of time. When such a problem must be solved on a message passing multiprocessor machine, the combination of these characteristics lead to system performance which decreases in time. Performance can be improved with periodic redistribution of computational load; however, redistribution can exact a sometimes large delay cost. We study the issue of deciding when to invoke a global load remapping mechanism. Such a decision policy must effectively weigh the costs of remapping against the performance benefits. We treat this problem by constructing two analytic models which exhibit stochastically decreasing performance. One model is quite tractable; we are able to describe the optimal remapping algorithm, and the optimal decision policy governing when to invoke that algorithm. However, computational complexity prohibits the use of the optimal remapping decision policy. We then study the performance of a general remapping policy on both analytic models. This policy attempts to minimize a statistic W(n) which measures the system degradation (including the cost of remapping) per computation step over a period of n steps. We show that as a function of time, the expected value of W(n) has at most one minimum, and that when this minimum exists it defines the optimal fixed-interval remapping policy. Our decision policy appeals to this result by remapping when it estimates that W(n) is minimized. Our performance data suggests that this policy effectively finds the natural frequency of remapping. We also use the analytic models to express the relationship between performance and remapping cost, number of processors, and the computation's stochastic activity.

Nicol, D. M.↗
DOE OSTI2017

Robust determination of the chemical potential in the pole expansion and selected inversion method for solving Kohn-Sham density functional theory

Fermi operator expansion (FOE) methods are powerful alternatives to diagonalization type methods for solving Kohn-Sham density functional theory (KSDFT). One example is the pole expansion and selected inversion (PEXSI) method, which approximates the Fermi operator by rational matrix functions and reduces the computational complexity to at most quadratic scaling for solving KSDFT. Unlike diagonalization type methods, the chemical potential often cannot be directly read off from the result of a single step of evaluation of the Fermi operator. Hence multiple evaluations are needed to be sequentially performed to compute the chemical potential to ensure the correct number of electrons within a given tolerance. This hinders the performance of FOE methods in practice. In this paper, we develop an efficient and robust strategy to determine the chemical potential in the context of the PEXSI method. The main idea of the new method is not to find the exact chemical potential at each self-consistent-field (SCF) iteration but to dynamically and rigorously update the upper and lower bounds for the true chemical potential, so that the chemical potential reaches its convergence along the SCF iteration. Instead of evaluating the Fermi operator for multiple times sequentially, our method uses a two-level strategy that evaluates the Fermi operators in parallel. In the regime of full parallelization, the wall clock time of each SCF iteration is always close to the time for one single evaluation of the Fermi operator, even when the initial guess is far away from the converged solution. We demonstrate the effectiveness of the new method using examples with metallic and insulating characters, as well as results from ab initio molecular dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1997

Systems Engineering Metrics: Organizational Complexity and Product Quality Modeling

Innovative organizational complexity and product quality models applicable to performance metrics for NASA-MSFC's Systems Analysis and Integration Laboratory (SAIL) missions and objectives are presented. An intensive research effort focuses on the synergistic combination of stochastic process modeling, nodal and spatial decomposition techniques, organizational and computational complexity, systems science and metrics, chaos, and proprietary statistical tools for accelerated risk assessment. This is followed by the development of a preliminary model, which is uniquely applicable and robust for quantitative purposes. Exercise of the preliminary model using a generic system hierarchy and the AXAF-I architectural hierarchy is provided. The Kendall test for positive dependence provides an initial verification and validation of the model. Finally, the research and development of the innovation is revisited, prior to peer review. This research and development effort results in near-term, measurable SAIL organizational and product quality methodologies, enhanced organizational risk assessment and evolutionary modeling results, and 91 improved statistical quantification of SAIL productivity interests.

Mog, Robert A.↗
NASA NTRS2024

Envisioning an Optimal Network of Space-Based Lasers for Orbital Debris Remediation

The rapid increase in resident space objects, including satellites and orbital debris, poses a significant threat to the safety and sustainability of space missions. This paper explores orbital debris remediation using a network of collaborative space-based lasers, leveraging laser ablation for momentum transfer on debris. A novel delta-v vector analysis framework quantifies the e↵ects of multiple simultaneous laser-to-debris (L2D) engagements by using vector composition of the imparted delta-v vectors. The paper introduces the Concurrent LocationScheduling Problem (CLSP), which optimizes the placement of laser platforms and the scheduling of L2D engagements to maximize debris remediation capacity. Due to the computational complexity of the CLSP, it is decomposed into two sequential subproblems: (1) optimal laser platform locations are determined using the Maximal Covering Location Problem, and (2) a novel integer linear programming-based approach schedules L2D engagements within the network configuration to maximize remediation capacity. Computational experiments are conducted to evaluate the proposed framework’s e↵ectiveness under various mission scenarios, demonstrating key network functions such as collaborative nudging, deorbiting, and just-in-time collision avoidance. A sensitivity analysis further examines how varying the number and distribution of laser platforms a↵ects debris remediation capacity, providing insights into optimizing the performance of space-based laser networks.

David O Williams Rogers↗
DOE OSTI2015

SU-E-T-355: Efficient Scatter Correction for Direct Ray-Tracing Based Dose Calculation

Purpose: To propose a scatter correction method with linear computational complexity for direct-ray-tracing (DRT) based dose calculation. Due to its speed and simplicity, DRT is widely used as a dose engine in the treatment planning system (TPS) and monitor unit (MU) verification software, where heterogeneity correction is applied by radiological distance scaling. However, such correction only accounts for attenuation but not scatter difference, causing the DRT algorithm less accurate than the model-based algorithms for small field size in heterogeneous media. Methods: Inspired by the convolution formula derived from an exponential kernel as is typically done in the collapsed-cone-convolution-superposition (CCCS) method, we redesigned the ray tracing component as the sum of TERMA scaled by a local deposition factor, which is linear with respect to density, and dose of the previous voxel scaled by a remote deposition factor, D(i)=aρ(i)T(i)+(b+c(ρ(i)-1))D(i-1),where T(i)=e(-αr(i)+β(r(i))2) and r(i)=Σ-(j=1,..,i)ρ(j).The two factors together with TERMA can be expressed in terms of 5 parameters, which are subsequently optimized by curve fitting using digital phantoms for each field size and each beam energy. Results: The proposed algorithm was implemented for the Fluence-Convolution-Broad-Beam (FCBB) dose engine and evaluated using digital slab phantoms and clinical CT data. Compared with the gold standard calculation, dose deviations were improved from 20% to 2% in the low density regions of the slab phantoms for the 1-cm field size, and within 2% for over 95% of the volume with the largest discrepancy at the interface for the clinical lung case. Conclusion: We developed a simple recursive formula for scatter correction for the DRT-based dose calculation with much improved accuracy, especially for small field size, while still keeping calculation to linear complexity. The proposed calculator is fast, yet accurate, which is crucial for dose updating in IMRT optimization.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Incremental principal component pursuit for video background modeling

An incremental Principal Component Pursuit (PCP) algorithm for video background modeling that is able to process one frame at a time while adapting to changes in background, with a computational complexity that allows for real-time processing, having a low memory footprint and is robust to translational and rotational jitter.

97 MATHEMATICS AND COMPUTING↗