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NASA NTRS2002

Effects of Ordering Strategies and Programming Paradigms on Sparse Matrix Computations

The Conjugate Gradient (CG) algorithm is perhaps the best-known iterative technique to solve sparse linear systems that are symmetric and positive definite. For systems that are ill-conditioned, it is often necessary to use a preconditioning technique. In this paper, we investigate the effects of various ordering and partitioning strategies on the performance of parallel CG and ILU(O) preconditioned CG (PCG) using different programming paradigms and architectures. Results show that for this class of applications: ordering significantly improves overall performance on both distributed and distributed shared-memory systems, that cache reuse may be more important than reducing communication, that it is possible to achieve message-passing performance using shared-memory constructs through careful data ordering and distribution, and that a hybrid MPI+OpenMP paradigm increases programming complexity with little performance gains. A implementation of CG on the Cray MTA does not require special ordering or partitioning to obtain high efficiency and scalability, giving it a distinct advantage for adaptive applications; however, it shows limited scalability for PCG due to a lack of thread level parallelism.

Oliker, Leonid↗

NASA NTRS2003

Subauditory Speech Recognition based on EMG/EPG Signals

Sub-vocal electromyogram/electro palatogram (EMG/EPG) signal classification is demonstrated as a method for silent speech recognition. Recorded electrode signals from the larynx and sublingual areas below the jaw are noise filtered and transformed into features using complex dual quad tree wavelet transforms. Feature sets for six sub-vocally pronounced words are trained using a trust region scaled conjugate gradient neural network. Real time signals for previously unseen patterns are classified into categories suitable for primitive control of graphic objects. Feature construction, recognition accuracy and an approach for extension of the technique to a variety of real world application areas are presented.

Jorgensen, Charles↗

NASA NTRS2004

Putting Priors in Mixture Density Mercer Kernels

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly infinite dimensional feature space. We describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using predefined kernels. These data adaptive kernels can en- code prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS). The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains template for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic- algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code. The results show that the Mixture Density Mercer-Kernel described here outperforms tree-based classification in distinguishing high-redshift galaxies from low- redshift galaxies by approximately 16% on test data, bagged trees by approximately 7%, and bagged trees built on a much larger sample of data by approximately 2%.

Srivastava, Ashok N.↗

NASA NTRS1999

User's Guide for ENSAERO_FE Parallel Finite Element Solver

A high fidelity parallel static structural analysis capability is created and interfaced to the multidisciplinary analysis package ENSAERO-MPI of Ames Research Center. This new module replaces ENSAERO's lower fidelity simple finite element and modal modules. Full aircraft structures may be more accurately modeled using the new finite element capability. Parallel computation is performed by breaking the full structure into multiple substructures. This approach is conceptually similar to ENSAERO's multizonal fluid analysis capability. The new substructure code is used to solve the structural finite element equations for each substructure in parallel. NASTRANKOSMIC is utilized as a front end for this code. Its full library of elements can be used to create an accurate and realistic aircraft model. It is used to create the stiffness matrices for each substructure. The new parallel code then uses an iterative preconditioned conjugate gradient method to solve the global structural equations for the substructure boundary nodes.

Eldred, Lloyd B.↗

NASA NTRS2004

Automatic Generation of Algorithms for the Statistical Analysis of Planetary Nebulae Images

Analyzing data sets collected in experiments or by observations is a Core scientific activity. Typically, experimentd and observational data are &aught with uncertainty, and the analysis is based on a statistical model of the conjectured underlying processes, The large data volumes collected by modern instruments make computer support indispensible for this. Consequently, scientists spend significant amounts of their time with the development and refinement of the data analysis programs. AutoBayes [GF+02, FS03] is a fully automatic synthesis system for generating statistical data analysis programs. Externally, it looks like a compiler: it takes an abstract problem specification and translates it into executable code. Its input is a concise description of a data analysis problem in the form of a statistical model as shown in Figure 1; its output is optimized and fully documented C/C++ code which can be linked dynamically into the Matlab and Octave environments. Internally, however, it is quite different: AutoBayes derives a customized algorithm implementing the given model using a schema-based process, and then further refines and optimizes the algorithm into code. A schema is a parameterized code template with associated semantic constraints which define and restrict the template s applicability. The schema parameters are instantiated in a problem-specific way during synthesis as AutoBayes checks the constraints against the original model or, recursively, against emerging sub-problems. AutoBayes schema library contains problem decomposition operators (which are justified by theorems in a formal logic in the domain of Bayesian networks) as well as machine learning algorithms (e.g., EM, k-Means) and nu- meric optimization methods (e.g., Nelder-Mead simplex, conjugate gradient). AutoBayes augments this schema-based approach by symbolic computation to derive closed-form solutions whenever possible. This is a major advantage over other statistical data analysis systems which use numerical approximations even in cases where closed-form solutions exist. AutoBayes is implemented in Prolog and comprises approximately 75.000 lines of code. In this paper, we take one typical scientific data analysis problem-analyzing planetary nebulae images taken by the Hubble Space Telescope-and show how AutoBayes can be used to automate the implementation of the necessary anal- ysis programs. We initially follow the analysis described by Knuth and Hajian [KHO2] and use AutoBayes to derive code for the published models. We show the details of the code derivation process, including the symbolic computations and automatic integration of library procedures, and compare the results of the automatically generated and manually implemented code. We then go beyond the original analysis and use AutoBayes to derive code for a simple image segmentation procedure based on a mixture model which can be used to automate a manual preproceesing step. Finally, we combine the original approach with the simple segmentation which yields a more detailed analysis. This also demonstrates that AutoBayes makes it easy to combine different aspects of data analysis.

Fischer, Bernd↗

NASA NTRS2005

On Modeling Air/Space-Borne Radar Returns in the Melting Layer

The bright band is the enhanced radar echo associated with the melting of hydrometeors in stratiform rain where the melting process usually occurs below 0 C isotherm over a distance of about 500m. To simulate this radar signature, a scattering model of melting snow is proposed in which the fractional water content is prescribed as a function of the radius of a spherical mixed- phase particle consisting of air, ice and water. The model is based on the observation that melting starts at the surface of the particle and then gradually develops towards the center. To compute the scattering parameters of a non-uniform melting particle, the particle is modeled as a sphere represented by a collection of 64(exp 3) cubic cells of identical size where the probability of water at any cell is prescribed as a function of the radius. The internal field of the particle, used for deriving the effective dielectric constant, is computed by the Conjugate Gradient and Fast Fourier Transform (CGFFT) numerical methods. To make computations of the scattering parameters more efficient, a multi-layer stratified-sphere scattering model is introduced after demonstrating that the scattering parameters of the non-uniformly melting particle can be accurately reproduced by the stratified sphere. In conjunction with a melting layer model that describes the melting fractions and fall velocities of hydrometeors as a function of the distance from the 0 C isotherm, the stratified-sphere model is used to simulate the radar bright band profiles. These simulated profiles are shown to compare well with measurements from the Precipitation Radar (PR) aboard the Tropical Rainfall Measuring Mission (TRMM) satellite and a dual-wavelength airborne radar. The results suggest that the proposed model of a melting snow particle may be useful in studying the characteristics of the bright-band in particular and mixed- phase hydrometeors in general.

Liao, Liang↗

NASA NTRS2005

An Ensemble Approach to Building Mercer Kernels with Prior Information

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly dimensional feature space. we describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using pre-defined kernels. These data adaptive kernels can encode prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. Specifically, we demonstrate the use of the algorithm in situations with extremely small samples of data. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS) and demonstrate the method's superior performance against standard methods. The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains templates for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic-algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code.

Srivastava, Ashok N.↗

NASA NTRS1996

Climate Data Assimilation on a Massively Parallel Supercomputer

We have designed and implemented a set of highly efficient and highly scalable algorithms for an unstructured computational package, the PSAS data assimilation package, as demonstrated by detailed performance analysis of systematic runs on up to 512-nodes of an Intel Paragon. The preconditioned Conjugate Gradient solver achieves a sustained 18 Gflops performance. Consequently, we achieve an unprecedented 100-fold reduction in time to solution on the Intel Paragon over a single head of a Cray C90. This not only exceeds the daily performance requirement of the Data Assimilation Office at NASA's Goddard Space Flight Center, but also makes it possible to explore much larger and challenging data assimilation problems which are unthinkable on a traditional computer platform such as the Cray C90.

supercomputer↗

NASA NTRS1995

A General Purpose Sparse Matrix Parallel Solvers Package

A general purpose solver package for constructing and solving a range of sparse linear systems arising from discretization of PDEs on unstructured meshes is developed. Once the sparse symmetric complex matrix is constructed, it can be solved by either a preconditioned bi-conjugate gradient solver, a two-stage Cholesky LDLT factorization solver, or a hybrid solver combining the above two methods.

solver sparse matrix solvers package PDE↗

NASA NTRS1995

A General Purpose Sparse Matrix Parallel Solvers Package

solver sparse matrix solvers package PDE↗

NASA NTRS2004

Using the GeoFEST Faulted Region Simulation System

GeoFEST (the Geophysical Finite Element Simulation Tool) simulates stress evolution, fault slip and plastic/elastic processes in realistic materials, and so is suitable for earthquake cycle studies in regions such as Southern California. Many new capabilities and means of access for GeoFEST are now supported. New abilities include MPI-based cluster parallel computing using automatic PYRAMID/Parmetis-based mesh partitioning, automatic mesh generation for layered media with rectangular faults, and results visualization that is integrated with remote sensing data. The parallel GeoFEST application has been successfully run on over a half-dozen computers, including Intel Xeon clusters, Itanium II and Altix machines, and the Apple G5 cluster. It is not separately optimized for different machines, but relies on good domain partitioning for load-balance and low communication, and careful writing of the parallel diagonally preconditioned conjugate gradient solver to keep communication overhead low. Demonstrated thousand-step solutions for over a million finite elements on 64 processors require under three hours, and scaling tests show high efficiency when using more than (order of) 4000 elements per processor. The source code and documentation for GeoFEST is available at no cost from Open Channel Foundation. In addition GeoFEST may be used through a browser-based portal environment available to approved users. That environment includes semi-automated geometry creation and mesh generation tools, GeoFEST, and RIVA-based visualization tools that include the ability to generate a flyover animation showing deformations and topography. Work is in progress to support simulation of a region with several faults using 16 million elements, using a strain energy metric to adapt the mesh to faithfully represent the solution in a region of widely varying strain.

Geophyical Finite Element Simulation Tool (GeoFEST↗

NASA NTRS2008

Application of Fast Multipole Methods to the NASA Fast Scattering Code

The NASA Fast Scattering Code (FSC) is a versatile noise prediction program designed to conduct aeroacoustic noise reduction studies. The equivalent source method is used to solve an exterior Helmholtz boundary value problem with an impedance type boundary condition. The solution process in FSC v2.0 requires direct manipulation of a large, dense system of linear equations, limiting the applicability of the code to small scales and/or moderate excitation frequencies. Recent advances in the use of Fast Multipole Methods (FMM) for solving scattering problems, coupled with sparse linear algebra techniques, suggest that a substantial reduction in computer resource utilization over conventional solution approaches can be obtained. Implementation of the single level FMM (SLFMM) and a variant of the Conjugate Gradient Method (CGM) into the FSC is discussed in this paper. The culmination of this effort, FSC v3.0, was used to generate solutions for three configurations of interest. Benchmarking against previously obtained simulations indicate that a twenty-fold reduction in computational memory and up to a four-fold reduction in computer time have been achieved on a single processor.

Dunn, Mark H.↗

NASA NTRS2009

The GMAO ADVAR System: Preliminary Results

The Goddard Earth Observing System (GEOS-S) Data Assimilation System is now configurable to run strong constraint 4DVAR. The system combines the 4DVAR-capable Grid-point Statistical Interpolation analysis with the GEOS-S general circulation model and an early version of the tangent linear and adjoint models of the finite-volume hydrodynamics with simplified physics. The GMAO 4DVAR uses a Lanczos-based conjugate gradient algorithm in a nested resolution inner-loop setting. A range of tests and experiments will have been carried out by the time of the Symposium. Results on balance-related issues, resolution configuration, and choice of assimilation time window will be shown. A comparison with the Global Modeling and Assimilation Office (GMAO) 3DVAR and a discussion of future directions of development will also be presented.

Todling, Ricardo↗

NASA NTRS2006

Magnetic Field Solver

The Magnetic Field Solver computer program calculates the magnetic field generated by a group of collinear, cylindrical axisymmetric electromagnet coils. Given the current flowing in, and the number of turns, axial position, and axial and radial dimensions of each coil, the program calculates matrix coefficients for a finite-difference system of equations that approximates a two-dimensional partial differential equation for the magnetic potential contributed by the coil. The program iteratively solves these finite-difference equations by use of the modified incomplete Cholesky preconditioned-conjugate-gradient method. The total magnetic potential as a function of axial (z) and radial (r) position is then calculated as a sum of the magnetic potentials of the individual coils, using a high-accuracy interpolation scheme. Then the r and z components of the magnetic field as functions of r and z are calculated from the total magnetic potential by use of a high-accuracy finite-difference scheme. Notably, for the finite-difference calculations, the program generates nonuniform two-dimensional computational meshes from nonuniform one-dimensional meshes. Each mesh is generated in such a way as to minimize the numerical error for a benchmark one-dimensional magnetostatic problem.

Ilin, Andrew V.↗

NASA NTRS2010

Improving Global Mass Flux Solutions from Gravity Recovery and Climate Experiment (GRACE) Through Forward Modeling and Continuous Time Correlation

We describe Earth's mass flux from April 2003 through November 2008 by deriving a time series of mas cons on a global 2deg x 2deg equal-area grid at 10 day intervals. We estimate the mass flux directly from K band range rate (KBRR) data provided by the Gravity Recovery and Climate Experiment (GRACE) mission. Using regularized least squares, we take into account the underlying process dynamics through continuous space and time-correlated constraints. In addition, we place the mascon approach in the context of other filtering techniques, showing its equivalence to anisotropic, nonsymmetric filtering, least squares collocation, and Kalman smoothing. We produce mascon time series from KBRR data that have and have not been corrected (forward modeled) for hydrological processes and fmd that the former produce superior results in oceanic areas by minimizing signal leakage from strong sources on land. By exploiting the structure of the spatiotemporal constraints, we are able to use a much more efficient (in storage and computation) inversion algorithm based upon the conjugate gradient method. This allows us to apply continuous rather than piecewise continuous time-correlated constraints, which we show via global maps and comparisons with ocean-bottom pressure gauges, to produce time series with reduced random variance and full systematic signal. Finally, we present a preferred global model, a hybrid whose oceanic portions are derived using forward modeling of hydrology but whose land portions are not, and thus represent a pure GRACE-derived signal.

Sabaka, T. J.↗

NASA NTRS2012

Failure Mode Analysis of V-Shaped Pyrotechnically Actuated Valves

Current V-shaped stainless steel pyrovalve initiators have rectified many of the deficiencies of the heritage Y-shaped aluminum design. However, a credible failure mode still exists for dual simultaneous initiator (NSI) firings in which low temperatures were detected at the booster cap and less consistent ignition was observed than when a single initiator was fired. In order to asses this issue, a numerical framework has been developed for predicting the flow through pyrotechnically actuated valves. This framework includes a fully coupled solution of the gas-phase equation with a non-equilibrium dispersed phase for solid particles as well as the capability to model conjugate gradient heat transfer to the booster cap. Through a hierarchy of increasingly complex simulations, a hypothesis for the failure mode of the nearly simultaneous dual NSI firings has been proven. The simulations indicate that the failure mode for simultaneous dual NSI firings may be caused by flow interactions between the flame channels. The shock waves from each initiator interact in the booster cavity resulting in a high pressure that prevents the gas and particulate velocity from rising in the booster cap region. This impedes the bulk of the particulate phase from impacting the booster cap and reduces the heat transfer to the booster cap since the particles do not impact it. Heat transfer calculations to the solid metal indicate that gas-phase convective heat transfer may not be adequate by itself and that energy transfer from the particulate phase may be crucial for the booster cap burn through.

Sachdev, Jai S.↗

NASA NTRS2012

The Atacama Cosmology Telescope: Data Characterization and Map Making

We present a description of the data reduction and mapmaking pipeline used for the 2008 observing season of the Atacama Cosmology Telescope (ACT). The data presented here at 148 GHz represent 12% or the 90 TB collected by ACT from 2007 to 2010. In 2008 we observed for 136 days, producing a total of 142h of data (11 TB for the 148 GHz band only), with a daily average of 10.5 h of observation. From these, 108.5 h were devoted to 850 sq deg stripe (11.2 h by 9 deg.1) centered on a declination of -52 deg.7, while 175 h were devoted to a 280 square deg stripe (4.5 h by 4 deg.8) centered at the celestial equator. We discuss sources of statistical and systematic noise, calibration, telescope pointing and data selection. Out of 1260 survey hours and 1024 detectors per array, 816 h and 593 effective detectors remain after data selection for this frequency band, yielding a 38 % survey efficiency. The total sensitivity in 2008, determined from the noise level between 5 Hz and 20 Hz in the time-ordered data stream (TOD), is 32 muK square root of s in CMB units. Atmospheric brightness fluctuations constitute the main contaminant in the data and dominate the detector and noise covariance at low frequencies in the TOD. The maps were made by solving the lease squares problem using the Preconditioned Conjugate Gradient method, incorporating the details of the detector and noise correlations. Cross-correlation with WMAP sky maps as well as analysis from simulations reveal the our maps are unbiased at l > 300. This paper accompanies the public release of the 148 GHz southern stripe maps from 2008. The techniques described here will be applied to future maps and data releases.

Duenner, Rolando↗

NASA NTRS2012

Estimating Sea Surface Salinity and Wind Using Combined Passive and Active L-Band Microwave Observations

Several L-band microwave radiometer and radar missions have been, or will be, operating in space for land and ocean observations. These include the NASA Aquarius mission and the Soil Moisture Active Passive (SMAP) mission, both of which use combined passive/ active L-band instruments. Aquarius s passive/active L-band microwave sensor has been designed to map the salinity field at the surface of the ocean from space. SMAP s primary objectives are for soil moisture and freeze/thaw detection, but it will operate continuously over the ocean, and hence will have significant potential for ocean surface research. In this innovation, an algorithm has been developed to retrieve simultaneously ocean surface salinity and wind from combined passive/active L-band microwave observations of sea surfaces. The algorithm takes advantage of the differing response of brightness temperatures and radar backscatter to salinity, wind speed, and direction, thus minimizing the least squares error (LSE) measure, which signifies the difference between measurements and model functions of brightness temperatures and radar backscatter. The algorithm uses the conjugate gradient method to search for the local minima of the LSE. Three LSE measures with different measurement combinations have been tested. The first LSE measure uses passive microwave data only with retrieval errors reaching 1 to 2 psu (practical salinity units) for salinity, and 1 to 2 m/s for wind speed. The second LSE measure uses both passive and active microwave data for vertical and horizontal polarizations. The addition of active microwave data significantly improves the retrieval accuracy by about a factor of five. To mitigate the impact of Faraday rotation on satellite observations, the third LSE measure uses measurement combinations invariant under the Faraday rotation. For Aquarius, the expected RMS SSS (sea surface salinity) error will be less than about 0.2 psu for low winds, and increases to 0.3 psu at 25 m/s wind speed for warm waters (25 C). To achieve the required 0.2 psu accuracy, the impact of sea surface roughness (e.g. wind-generated ripples) on the observed brightness temperature has to be corrected to better than one tenth of a degree Kelvin. With this algorithm, the accuracy of retrieved wind speed will be high, varying from a few tenths to 0.6 m/s. The expected direction accuracy is also excellent (less than 10 ) for mid to high winds, but degrades for lower speeds (less than 7 m/s).

Yueh, Simon H.↗