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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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At least 397 records · Page 22
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Interval Predictor Models for Robust System Identification

This paper proposes a framework for the identification and uncertainty quantification of plant models according to multivariable data. The only restriction imposed upon such models is for their outputs to depend continuously on their parameters. An Interval Predictor Model (IPM) prescribes the parameters of a computational model as a path-connected set thereby making each predicted output an interval-valued function of its inputs. The formulation proposed seeks the parameter set for which the predicted outputs tightly enclose the data. This set, which is modeled as a semi-algebraic set of low-degree polynomials, enables the characterization of possibly strong parameter dependencies commonly found in practice. This uncertainty characterization makes the resulting plant model amenable to robust control approaches using polynomial optimization. Furthermore, we use non-convex scenario theory to assess the reliability of the resulting IPM. This assessment yields a distribution-free upper bound on the probability that future data will fall outside the predicted intervals.

interval↗
DOE OSTI2020

ROM-Based Surrogate Systems Modeling of EBR-II

We report the System Analysis Module (SAM), developed and maintained by Argonne National Laboratory, is designed to provide whole-plant transient safety analysis capabilities for a number of advanced non-light water reactors, including sodium-cooled fast reactor (SFR), lead-cooled fast reactor (LFR), and molten salt reactor (MSR)/fluoride-salt-cooled high-temperature reactor (FHR) designs. SAM is primarily constructed as a systems-level analysis tool, with the potential to incorporate reduced order models from three-dimensional computational fluid dynamics (CFD) simulations to improve characterization of complex, multidimensional physics. It is recognized that the computational expense associated with CFD can be intractable for various engineering analyses, such as uncertainty quantification, inference, and design optimization. This paper explores the reducibility of a SAM model using recent advances in randomized linear algebra techniques, which attempt to find recurring patterns in the various realizations generated by a model after randomly perturbing all its input parameters. The reduction is described in terms of fewer degrees of freedom (DOFs), referred to as the active DOFs, for the model variables such as input model parameters and model responses. The results indicate that there is significant room for additional reduction that may be leveraged for additional computational gains when employing SAM for engineering-intensive analyses that require repeated model executions. Different from physics-based reduction approaches, the proposed approach allows one to estimate upper bounds on the reduction errors, which are rigorously developed in this work. Finally, different methods for surrogate model construction, such as regression and neural network-based training, are employed to correlate the input and output active DOFs, which are related back to the original variables using matrix-based linear transformations.

42 ENGINEERING↗
DOE OSTI2022

Performance and power modeling and prediction using MuMMI and 10 machine learning methods

Energy-efficient scientific applications require insight into how high performance computing system features impact the applications' power and performance. This insight can result from the development of performance and power models. Here, in this article, we use the modeling and prediction tool MuMMI (Multiple Metrics Modeling Infrastructure) and 10 machine learning methods to model and predict performance and power consumption and compare their prediction error rates. We use an algorithm-based fault-tolerant linear algebra code and a multilevel checkpointing fault-tolerant heat distribution code to conduct our modeling and prediction study on the Cray XC40 Theta and IBM BG/Q Mira at Argonne National Laboratory and the Intel Haswell cluster Shepard at Sandia National Laboratories. Our experimental results show that the prediction error rates in performance and power using MuMMI are less than 10% for most cases. By utilizing the models for runtime, node power, CPU power, and memory power, we identify the most significant performance counters for potential application optimizations, and we predict theoretical outcomes of the optimizations. Based on two collected datasets, we analyze and compare the prediction accuracy in performance and power consumption using MuMMI and 10 machine learning methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

The influence of interval arithmetic on the shape of uncertainly defined domains modelled by closed curves

The paper presents an unambiguous modelling of imprecisely defined shapes of closed curves using classical and directed interval arithmetic. The authors focus on the development of an effective strategy of modelling interval smooth closed curves (which enforce C{sup 2} continuity in points at which adjacent interval segments join) using interval cubic Bézier segments. For this purpose, algebraic relationships between Bézier and de Boor control points, formerly known for precisely defined curves, are generalized. We obtain interval control points that define interval closed curves. Additionally, the reliability of such way of modelling of closed curves is examined. We directly apply classical and directed interval arithmetic to mentioned relationships and try to solve obtained interval systems of algebraic equations. However, we obtain ambiguous solutions. Therefore, we propose our new strategy of modification of directed interval arithmetic to obtain reliable and unambiguous shapes of interval closed curves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Derivation of K-matrix reaction theory in a discrete basis formalism

The usual derivations of the S and K matrices for two-particle reactions proceed through the Lippmann–Schwinger equation with formal definitions of the incoming and outgoing scattering states. Here we present a simpler alternative derivation that is carried out completely in the Hamiltonian representation, using a discrete basis of configurations for the scattering channels as well as the quasi-bound configurations of the combined fragments. We use matrix algebra to derive an explicit expression for the K matrix in terms of the Hamiltonian of the internal states of the compound system and the coupling between the channels and the internal states. The formula for the K matrix includes explicitly a real dispersive shift matrix to the internal Hamiltonian that is easily computed in the formalism. That expression is applied to derive the usual form of the S matrix as a sum over poles in the complex energy plane. Some extensions and limitations of the discrete-basis Hamiltonian formalism are discussed in the concluding remarks and in the Appendix.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Attacking the Opioid Epidemic: Determining the Epistatic and Pleiotropic Genetic Architectures for Chronic Pain and Opioid Addiction

We describe the CoMet application for large-scale epistatic Genome-Wide Association Studies (eGWAS) and pleiotropy studies. High performance is attained by transforming the underlying vector comparison methods into highly performant generalized distributed dense linear algebra operations. The 2-way and 3-way Proportional Similarity metric and Custom Correlation Coefficient are implemented using native or adapted GEMM kernels optimized for GPU architectures. By aggressive overlapping of communications, transfers and computations, high efficiency with respect to single GPU kernel performance is maintained up to the full Titan and Summit systems. Nearly 300 quadrillion element comparisons per second and over 2.3 mixed precision ExaOps are reached on Summit by use of Tensor Core hardware on the Nvidia Volta GPUs. Performance is four to five orders of magnitude beyond comparable state of the art. CoMet is currently being used in projects ranging from bioenergy to clinical genomics, including for the genetics of chronic pain and opioid addiction.

Joubert, Wayne↗
NASA NTRS1977

Symbolic computer vector analysis

A MACSYMA program is described which performs symbolic vector algebra and vector calculus. The program can combine and simplify symbolic expressions including dot products and cross products, together with the gradient, divergence, curl, and Laplacian operators. The distribution of these operators over sums or products is under user control, as are various other expansions, including expansion into components in any specific orthogonal coordinate system. There is also a capability for deriving the scalar or vector potential of a vector field. Examples include derivation of the partial differential equations describing fluid flow and magnetohydrodynamics, for 12 different classic orthogonal curvilinear coordinate systems.

Stoutemyer, D. R.↗
NASA NTRS2009

Aerothermal Testing for Project Orion Crew Exploration Vehicle

The Project Orion Crew Exploration Vehicle aerothermodynamic experimentation strategy, as it relates to flight database development, is reviewed. Experimental data has been obtained to both validate the computational predictions utilized as part of the database and support the development of engineering models for issues not adequately addressed with computations. An outline is provided of the working groups formed to address the key deficiencies in data and knowledge for blunt reentry vehicles. The facilities utilized to address these deficiencies are reviewed, along with some of the important results obtained thus far. For smooth wall comparisons of computational convective heating predictions against experimental data from several facilities, confidence was gained with the use of algebraic turbulence model solutions as part of the database. For cavities and protuberances, experimental data is being used for screening various designs, plus providing support to the development of engineering models. With the reaction-control system testing, experimental data were acquired on the surface in combination with off-body flow visualization of the jet plumes and interactions. These results are being compared against predictions for improved understanding of aftbody thermal environments and uncertainties.

Berry, Scott A.↗
DOE OSTI2021

Improving scalability of electronic structure code for molecular simulations in the presence of environment

A scalable density functional electronic code with Gaussian basis set, called UTEP-NRLMOL, is developed to perform simulations of molecular systems in the presence of the environment with particular attention to the memory requirements. In the electronic structure calculations, the memory and computation time are proportional to the number of atoms. Memory requirements for density functional calculations scale as N*N, where N is the number of atoms. While the recent advances in HPC offer platforms with large numbers of cores, the limited amount of memory available on a given node and poor scalability of the electronic structure codes hinder their efficient usage of these platforms. We have introduced new scaling and parallelization paradigms using MPI-3 shared-memory functionality combined with usage of sparse algebra and storage of matrices in sparse format. This extends the range of applicability of the UTEP-NRLMOL code to large systems over 10,000 atoms, or using up to 67,000 basis functions, and making use of HPC architectures using over 6,000 processors utilizing all available cores. We have also interfaced code with effective fragment potential and polarizable continuum model libraries. The code was used in simulations of several applications which are published in reputed scientific journals.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2017

Computing the non-Markovian coarse-grained interactions derived from the Mori–Zwanzig formalism in molecular systems: Application to polymer melts

Memory effects are often presented during coarse-graining of a complex dynamical system. In particular, a generalized Langevin equation (GLE) for the coarse-grained (CG) system arises in the context of Mori–Zwanzig formalism. Upon a pairwise decomposition, GLE can be reformulated into its pairwise version, i.e., non-Markovian dissipative particle dynamics (DPD). GLE models the dynamics of a single coarse particle, while DPD considers the dynamics of many interacting CG particles, with both CG systems governed by non-Markovian interactions. We compare two different methods for the practical implementation of the non-Markovian interactions in GLE and DPD systems. In particular, a direct evaluation of the non-Markovian (NM) terms is performed in LE-NM and DPD-NM models, which requires the storage of historical information that significantly increases computational complexity. Alternatively, we use a few auxiliary variables in LE-AUX and DPD-AUX models to replace the non-Markovian dynamics with a Markovian dynamics in a higher dimensional space, leading to a much reduced memory footprint and computational cost. In our numerical benchmarks, the GLE and non-Markovian DPD models are constructed from molecular dynamics (MD) simulations of star-polymer melts. Results show that a Markovian dynamics with auxiliary variables successfully generates equivalent non-Markovian dynamics consistent with the reference MD system, while maintaining a tractable computational cost. Also, transient subdiffusion of the star-polymers observed in the MD system can be reproduced by the coarse-grained models. The non-interacting particle models, LE-NM/AUX, are computationally much cheaper than the interacting particle models, DPD-NM/AUX. Yet, the pairwise models with momentum conservation are more appropriate for correctly reproducing the long-time hydrodynamics characterised by an algebraic decay in the velocity autocorrelation function.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

One dimensional staggered bosons, clock models, and their noninvertible symmetries

We study systems of staggered boson Hamiltonians in a one dimensional lattice and in particular how the translation symmetry by one unit in these systems is in reality a noninvertible symmetry closely related to T-duality. We also study the simplest systems of clock models derived from these staggered boson Hamiltonians. We show that the noninvertible symmetries of these lattice models together with the discrete Z N symmetry predict that these are critical points with a U ( 1 ) current algebra at c = 1 and radius 2 N whenever N > 4 . We also present an independent computation of this value that arises directly from the staggered boson variables and does not use these additional symmetries. We also present a theoretical estimate of the values of critical coupling constants away from the self-dual symmetry point in these clock models. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
NASA NTRS1975

Computer-developed construction of analytic expressions for the coordinates and partial derivatives of Jupiter's Galilean satellites

A method for improving Sampson's (1910, 1912, 1921) original work in developing series expressions for accurate coordinates of the Galilean satellites is discussed. The method, which utilizes computer-based algebraic manipulation software, was developed to reconstruct Sampson's theory, remove existing errors, introduce neglected effects, and provide analytic expressions for the coordinates as well as for the partial derivatives with respect to orbital parameters, Jupiter's mass and oblateness, the satellite masses, and Jupiter's pole and rotation period. The software system, capable of handling Poisson series with up to 73 polynomial variables and 28 trigonometric arguments, is described. The preliminary solution is presented, and procedures are outlined for calculating perturbations and eliminating auxiliary parameters.

Lieske, J. H.↗
NASA NTRS1986

Time scale analysis of a closed-loop discrete optimal control system

A two-time scale discrete control system is considered. The closed-loop optimal linear quadratic (LQ) regulator for the system requires the solution of a full-order algebraic matrix Riccati equation. Alternatively, the original system is decomposed into reduced-order slow and fast subsystems. The closed-loop optimal control of the subsystems requires the solution of two algebraic matrix Riccati equations of order lower than that required for the full-order system. A composite, closed-loop suboptimal control is created from the sum of the slow and fast feedback optimal controls. Numerical results obtained for an aircraft model show a very close agreement between the exact (optimal) solutions and computationally simpler composite (suboptimal) solutions. The main advantage of the method is the considerable reduction in the overall computational requirements for the closed-loop optimal control of digital flight systems.

Naidu, D. S.↗
DOE OSTI2018

Divisible Rigid Groups. II. Stability, Saturation, and Elementary Submodels

A group G is said to be rigid if it contains a normal series G = G{sub 1} > G{sub 2} > . . . > G{sub m} > G{sub m+1} = 1, whose quotients G{sub i}/G{sub i+1} are Abelian and, treated as right ℤ[G/G{sub i}]- modules, are torsion-free. A rigid group G is divisible if elements of the quotient G{sub i}/G{sub i+1} are divisible by nonzero elements of the ring ℤ[G/G{sub i}]. Every rigid group is embedded in a divisible one. Previously, it was stated that the theory 𝔗{sub m} of divisible m-rigid groups is complete. Here, it is proved that this theory is ω-stable. Furthermore, we describe saturated models, study elementary submodels of an arbitrary model, and find a representation for a countable saturated model in the form of a limit group in the Fraïssé system of all finitely generated m-rigid groups. Also, it is proved that the theory 𝔗{sub m} admits quantifier elimination down to a Boolean combination of ∀∃-formulas.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Numerical solution of systems of fractional delay differential equations using a new kind of wavelet basis

In the present paper, a new orthonormal wavelet basis, called Chelyshkov wavelet, is constructed from a class of orthonormal polynomials. These wavelet basis and their properties are utilized to obtain their operational matrix of fractional integration in the Riemann–Liouville sense and delay operational matrix. Convergence and error bound of the expansion by this kind of wavelet functions are investigated. Then, these operational matrices along with the Galerkin approach have been implemented to solve systems of fractional delay differential equations (SFDDEs). The main superiority of the proposed technique is that it reduces SFDDEs to a system of algebraic equations. Moreover, accuracy and efficiency of the suggested Chelyshkov wavelet approach are verified through some linear and nonlinear SFDDEs. Finally, the obtained numerical results are compared with those previously reported in the literature.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

Development of guidelines for the definition of the relavant information content in data classes

The problem of experiment design is defined as an information system consisting of information source, measurement unit, environmental disturbances, data handling and storage, and the mathematical analysis and usage of data. Based on today's concept of effective computability, general guidelines for the definition of the relevant information content in data classes are derived. The lack of a universally applicable information theory and corresponding mathematical or system structure is restricting the solvable problem classes to a small set. It is expected that a new relativity theory of information, generally described by a universal algebra of relations will lead to new mathematical models and system structures capable of modeling any well defined practical problem isomorphic to an equivalence relation at any corresponding level of abstractness.

Schmitt, E.↗
DOE OSTI2024

MAGMA: Enabling exascale performance with accelerated BLAS and LAPACK for diverse GPU architectures

MAGMA (Matrix Algebra for GPU and Multicore Architectures) is a pivotal open-source library in the landscape of GPU-enabled dense and sparse linear algebra computations. With a repertoire of approximately 750 numerical routines across four precisions, MAGMA is deeply ingrained in the DOE software stack, playing a crucial role in high-performance computing. Notable projects such as ExaConstit, HiOP, MARBL, and STRUMPACK, among others, directly harness the capabilities of MAGMA. In addition, the MAGMA development team has been acknowledged multiple times for contributing to the vendors’ numerical software stacks. Looking back over the time of the Exascale Computing Project (ECP), we highlight how MAGMA has adapted to recent changes in modern HPC systems, especially the growing gap between CPU and GPU compute capabilities, as well as the introduction of low precision arithmetic in modern GPUs. We also describe MAGMA’s direct impact on several ECP projects. Maintaining portable performance across NVIDIA and AMD GPUs, and with current efforts toward supporting Intel GPUs, MAGMA ensures its adaptability and relevance in the ever-evolving landscape of GPU architectures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Low-order preconditioning of the Stokes equations

A well-known strategy for building effective preconditioners for higher-order discretizations of some PDEs, such as Poisson's equation, is to leverage effective preconditioners for their low-order analogs. In this work, we show that high-quality preconditioners can also be derived for the Taylor–Hood discretization of the Stokes equations in much the same manner. In particular, we investigate the use of geometric multigrid based on the Q 1 iso Q 2 /Q 1 discretization of the Stokes operator as a preconditioner for the Q 2 /Q 1 discretization of the Stokes system. We utilize local Fourier analysis to optimize the damping parameters for Vanka and Braess–Sarazin relaxation schemes and to achieve robust convergence. Furthermore, these results are then verified and compared against the measured multigrid performance. While geometric multigrid can be applied directly to the Q 2 /Q 1 system, our ultimate motivation is to apply algebraic multigrid within solvers for Q 2 /Q 1 systems via the Q 1 iso Q 2 /Q 1 discretization, which will be considered in a companion paper.

97 MATHEMATICS AND COMPUTING↗