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DOE OSTI2020

Systematic Assessment of Retrieval Methods for Canopy Far-Red Solar-Induced Chlorophyll Fluorescence Using High-Frequency Automated Field Spectroscopy

Remote sensing of solar-induced chlorophyll fluorescence (SIF) offers potential to infer photosynthesis across scales and biomes. Many retrieval methods have been developed to estimate top-of-canopy SIF using ground-based spectroscopy. However, inconsistencies among methods may confound interpretation of SIF dynamics, eco-physiological/environmental drivers, and its relationship with photosynthesis. Using high temporal- and spectral resolution ground-based spectroscopy, we aimed to (1) evaluate performance of SIF retrieval methods under diverse sky conditions using continuous field measurements; (2) assess method sensitivity to fluctuating light, reflectance, and fluorescence emission spectra; and (3) inform users for optimal ground-based SIF retrieval. Analysis included field measurements from bi-hemispherical and hemispherical-conical systems and synthetic upwelling radiance constructed from measured downwelling radiance, simulated reflectance, and simulated fluorescence for benchmarking. Fraunhofer-based differential optical absorption spectroscopy (DOAS) and singular vector decomposition (SVD) retrievals exhibit convergent SIF-PAR relationships and diurnal consistency across different sky conditions, while O2A-based spectral fitting method (SFM), SVD, and modified Fraunhofer line discrimination (3FLD) exhibit divergent SIF-PAR relationships across sky conditions. We find that such behavior holds across system configurations, though hemispherical-conical systems diverge less across sky conditions. O 2 A retrieval accuracy, influenced by atmospheric distortion, improves with a narrower fitting window and when training SVD with temporally local spectra. This may impact SIF-photosynthesis relationships interpreted by previous studies using O 2 A-based retrievals with standard (759–767.76 nm) fitting windows. Fraunhofer-based retrievals resist atmospheric impacts but are noisier and more sensitive to assumed SIF spectral shape than O 2 A-based retrievals. We recommend SVD or SFM using reduced fitting window (759.5–761.5 nm) for robust far-red SIF retrievals across sky conditions.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Exploring Hilbert space on a budget: Novel benchmark set and performance metric for testing electronic structure methods in the regime of strong correlation

This work explores the ability of classical electronic structure methods to efficiently represent (compress) the information content of full configuration interaction (FCI) wave functions. We introduce a benchmark set of four hydrogen model systems of different dimensionalities and distinctive electronic structures: a 1D chain, a 1D ring, a 2D triangular lattice, and a 3D close-packed pyramid. To assess the ability of a computational method to produce accurate and compact wave functions, we introduce the accuracy volume, a metric that measures the number of variational parameters necessary to achieve a target energy error. Using this metric and the hydrogen models, we examine the performance of three classical deterministic methods: (i) selected configuration interaction (sCI) realized both via an a posteriori (ap-sCI) and variational selection of the most important determinants, (ii) an a posteriori singular value decomposition (SVD) of the FCI tensor (SVD-FCI), and (iii) the matrix product state representation obtained via the density matrix renormalization group (DMRG). We find that the DMRG generally gives the most efficient wave function representation for all systems, particularly in the 1D chain with a localized basis. For the 2D and 3D systems, all methods (except DMRG) perform best with a delocalized basis, and the efficiency of sCI and SVD-FCI is closer to that of DMRG. For larger analogs of the models, the DMRG consistently requires the fewest parameters but still scales exponentially in 2D and 3D systems, and the performance of SVD-FCI is essentially equivalent to that of ap-sCI.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

A Survey of Singular Value Decomposition Methods for Distributed Tall/Skinny Data

The Singular Value Decomposition (SVD) is one of the most important matrix factorizations, enjoying a wide variety of applications across numerous application domains. In statistics and data analysis, the common applications of SVD inclue Principal Components Analysis (PCA) and regression. Usually these applications arise on data that has far more rows than columns, so-called "tall/skinny" matrices. In the big data analytics context, this may take the form of hundreds of millions to billions of rows with only a few hundred columns. There is a need, therefore, for fast, accurate, and scalable tall/skinny SVD implementations which can fully utilize modern computing resources. To that end, we present a survey of three different algorithms for computing the SVD for these kinds of tall/skinny data layouts using MPI for communication. We contextualize these with common big data analytics techniques. Finally, we present both CPU and GPU timing results from the Summit supercomputer, and discuss possible alternative approaches.

Schmidt, Drew↗

DOE OSTI2020

Integrated Approach to Investigating Historic Cemeteries

Ground-penetrating radar (GPR) and terrestrial laser scanning (TLS) surveys were conducted at a historic cemetery at Cape Canaveral Air Force Station, Florida, U.S., in order to confirm the presence of burials corresponding to grave markers and detect potential unmarked burials. Noise in the GPR data from surface features and subtle terrain differences must be addressed to determine the extent of anomalies of interest. We use singular value decomposition (SVD) to isolate and remove energy from GPR data. SVD allows one to remove unwanted signals that traditional processing techniques cannot. With SVD filtering, we resolve an anomaly adjacent to confirmed burials otherwise overprinted by unwanted signal. The migration of SVD-filtered data produces more distinct, spatially constrained point reflectors. Ground elevation is derived from georeferenced TLS data and compared to that from airborne laser scanning (ALS) to highlight subtle terrain that can assist data interpretation. TLS elevations show a subtle modern mound over the burial plot where ALS elevations show a depression. The targets of interest are approximately 20–30 cm higher in elevation if a topographic correction is performed using TLS versus ALS. In archaeological applications, a notable change is often recorded at the sub-meter scale. The combined approach presented here better resolves geophysical response of buried features and their positions in the ground relative to each other.

Downs, Christine (ORCID:0000000237229381)↗

NASA NTRS2002

Development of an Efficient Binaural Simulation for the Analysis of Structural Acoustic Data

Binaural or "virtual acoustic" representation has been proposed as a method of analyzing acoustic and vibroacoustic data. Unfortunately, this binaural representation can require extensive computer power to apply the Head Related Transfer Functions (HRTFs) to a large number of sources, as with a vibrating structure. This work focuses on reducing the number of real-time computations required in this binaural analysis through the use of Singular Value Decomposition (SVD) and Equivalent Source Reduction (ESR). The SVD method reduces the complexity of the HRTF computations by breaking the HRTFs into dominant singular values (and vectors). The ESR method reduces the number of sources to be analyzed in real-time computation by replacing sources on the scale of a structural wavelength with sources on the scale of an acoustic wavelength. It is shown that the effectiveness of the SVD and ESR methods improves as the complexity of the source increases. In addition, preliminary auralization tests have shown that the results from both the SVD and ESR methods are indistinguishable from the results found with the exhaustive method.

Lalime, Aimee L.↗

NASA NTRSDate not supplied

Dynamic Mode Decomposition of Unsteady Pressure-Sensitive Paint Measurements for the NASA Unitary Plan Wind Tunnel Tests

This paper describes the Dynamic Mode Decomposition (DMD) of the pressures on the scale model of the Space Launch System (SLS) Block 1 cargo vehicle with the Unsteady Pressure-Sensitive Paint (uPSP) measurements, which were collected in the Ascent Transient Aerodynamics Tests with the Unitary Plan Wind Tunnel 11-by-11-foot Transonic Wind Tunnel in September 2019 at NASA Ames Research Center. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. The conventional DMD algorithm is based on the Singular Value Decomposition (SVD) of the data matrix. For the matrix of the uPSP measurements of the SLS ATAT, the number of rows is equal to the number of nodes in the grid of the scale model, and the number of columns is equal to the number of frames in the videos taken with 4 Phantom high-speed cameras. In this paper, it is verified that, for the time series with zero mean value, the DMD is equivalent to the decomposition with the Discrete Fourier Transform (DFT). Considering the uPSP is mainly used in the assessment of the unsteady, aerodynamic phenomena, the DMD of the uPSP measurements can be implemented in two steps: (1) subtract the mean value from the uPSP measurement on each of the grid nodes; (2) apply the Fast Fourier Transform (FFT) on the resulting zero-mean time series. The DMD of the uPSP measurements with FFT has two advantages: (1) the computational complexity of FFT is O(N*logN), where N is the length of the time series; (2) compared to the SVD-based DMD algorithm, the DMD with FFT can be easily implemented in parallel processing. A sample matrix of uPSP measurements, at the size of 341 grid nodes and 128 frames, is generated. Figures 1 and 2 show the eigenvalues and the ratios of the eigenvectors, respectively, of the sample matrix, without and with the mean value removed on each of the grid nodes, computed with the SVD-based DMD and the FFT. The figures demonstrate the equivalence of the SVD-based DMD and the decomposition with DFT/FFT for the time series with zero mean value. The results of DMD of the uPSP measurements of the SLS ATAT in September 2019 are presented in the paper. The DMD modes at different frequencies are shown, the aerodynamic phenomena (e.g. shockwave and vortex shedding) are demonstrated and the correlation of the DMD modes with the test configuration parameter (e.g., the Mach Number) is discussed. Figure 3 shows a software tool to visualize the DMD modes. The code to implement the algorithm described in this paper was written in C, with libraries of FFTW for FFT and MPI/OpenMP for parallel processing, and executed on the NASA Pleiades supercomputer. Funding for this research was provided by the NASA Aerosciences Evaluation and Test Capabilities Project.

Pressure-Sensitive Paint↗

NASA NTRSDate not supplied

Active Thermography Based on Tensor Rank Decomposition

Principal Component Thermography applies Singular Value Decomposition (SVD) to post-process data that are derived from active thermographic inspections. SVD provides useful compression of the data and allows for better understanding of substructure and indications of potential damage. In the standard approach, SVD is applied to a certain reshaping of a three-dimensional data stack into a two-dimensional array. This work applies the CANDECOMP-PARAFAC (CP) tensor rank decomposition directly to the three-dimensional data to avoid the initial reshaping step in order to begin to develop an inspection method that can more accurately detect defects in non-homogeneous and anisotropic materials. Tests against simulated data that compare the CP decomposition method with traditional Principal Component Thermography based on SVD are described. Finally, the method of Proper Generalized Decomposition (PGD) is used to derive the CP decomposition, and its performance against other algorithms is also discussed.

Thermography↗

DOE OSTI2020

Singular value decomposition of adjoint flux distributions for Monte Carlo variance reduction

Monte Carlo (MC) shielding calculations often use weight windows (WWs) and biased sources formed from a deterministic estimate of the adjoint flux to improve the convergence rate of tallies. This requires a significant amount of computer memory, which can limit the memory available for high-resolution tally output. A new method is proposed for reducing these memory requirements by using singular value decomposition (SVD) in linear or logarithmic space to approximate the adjoint flux. This method’s performance is evaluated using the Shift and Denovo codes for streaming and diffusion base case problems, followed by problems using the Westinghouse AP1000 and the Joint European Torus. The log SVD reduced WW memory requirements by an order of magnitude in all cases without a significant performance penalty. Additionally, the linear SVD reduced biased source memory requirements by an order of magnitude, but further investigation is needed to account for observed limitations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Compression of tokamak boundary plasma simulation data using a maximum volume algorithm for matrix skeleton decomposition

This report demonstrates satisfactory data compression of SOLPS-ITER simulation output ranging from 2D fields, 1D profiles, and 0D scalar variables with a novel matrix decomposition approach. The singular value decomposition (SVD) scales poorly for large matrix sizes and is unsuited to the application on high dimensional data common to fusion plasma physics simulation. In this work, we employ the columns-submatrix-rows (CUR) matrix factorization technique in order to compute a low-rank approximation up to two orders of magnitude faster than the SVD, but within a nominal L2-norm relative error of ε = 10 –2 . In addition, the CUR approach maintains the original format of the data, in its extracted columns and rows, allowing for interpretable data storage at the original resolution of the simulation. We utilize an iterative algorithm to compute the CUR decomposition of simulation output by maximizing the volume, or linearly independent information content, of a low-rank submatrix contained within the data. Experiments over $\textit{n} × \textit{n}$ randomized test matrices with embedded rank-deficient features show that this maximum volume implementation of CUR matrix approximation has reduced asymptotic computational complexity on the order of n compared to the SVD, which scales approximately as $n^3$. These results show that the CUR technique can be used to effectively select time step snapshots (columns) of over 140 SOLPS-ITER output variables and the associated discretized coordinate timeseries (rows) allowing for reconstruction of the complete simulation dynamics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

PythonFOAM: In-situ data analyses with OpenFOAM and Python

Here, we outline the development of a general-purpose Python-based data analysis tool for OpenFOAM. Our implementation relies on the construction of OpenFOAM applications that have bindings to data analysis libraries in Python. Double precision data in OpenFOAM is cast to a NumPy array using the NumPy C-API and Python modules may then be used for arbitrary data analysis and manipulation on flow-field information. We highlight how the proposed wrapper may be used for an in-situ online singular value decomposition (SVD) implemented in Python and accessed from the OpenFOAM solver PimpleFOAM. Here, 'in-situ' refers to a programming paradigm that allows for a concurrent computation of the data analysis on the same computational resources utilized for the partial differential equation solver. In addition, to demonstrate parallel deployments, we deploy a distributed SVD, which collects snapshot data across the ranks of a distributed simulation to compute the global left singular vectors. Crucially, both OpenFOAM and Python share the same message passing interface (MPI) communicator for this deployment which allows Python objects and functions to exchange NumPy arrays across ranks. Subsequently, we provide scaling assessments of this distributed SVD on multiple nodes of Intel Broadwell and KNL architectures for canonical test cases such as the large eddy simulations of a backward facing step and a channel flow at friction Reynolds number of 395. Finally, we demonstrate the deployment of a deep neural network for compressing the flow-field information using an autoencoder to demonstrate an ability to use state-of-the-art machine learning tools in the Python ecosystem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Deep learning for in situ data compression of large turbulent flow simulations

As the size of turbulent flow simulations continues to grow, in situ data compression is becoming increasingly important for visualization, analysis, and restart checkpointing. For these applications, single-pass compression techniques with low computational and communication overhead are crucial. In this paper we present a deep-learning approach to in situ compression using an autoencoder architecture that is customized for three-dimensional turbulent flows and is well suited for contemporary heterogeneous computing resources. The autoencoder is compared against a recently introduced randomized single-pass singular value decomposition (SVD) for three different canonical turbulent flows: decaying homogeneous isotropic turbulence, a Taylor-Green vortex, and turbulent channel flow. Our proposed fully convolutional autoencoder architecture compresses turbulent flow snapshots by a factor of 64 with a single pass, allows for arbitrarily sized input fields, is cheaper to compute than the randomized single-pass SVD for typical simulation sizes, performs well on unseen flow configurations, and has been made publicly available. The results reported here show that the autoencoder dramatically outperforms a randomized single-pass SVD with similar compression ratio and yields comparable performance to a higher-rank decomposition with an order of magnitude less compression in regard to preserving a number of important statistical quantities such as turbulent kinetic energy, enstrophy, and Reynolds stresses.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

AEflow (Autoencoder fluid flow compression network) [SWR-22-29]

King, Ryan↗

NASA NTRS1988

Applications of square-root information filtering and smoothing in spacecraft orbit determination

The JPL (Jet Propulsion Laboratory) Orbit Determination Software System is a set of computer programs developed for the primary purpose of determining the flight path of deep-space mission spacecraft in NASA's Planetary Program and highly elliptical orbiting spacecraft in Earth orbit. The filtering processes available within the JPL Orbit Determination Software are discussed, and several examples are presented. In particular, solutions obtained by the Square Root Information Filter (SRIF) using Bierman's Estimation Subroutine Library (ESL) are discussed and compared with the solutions obtained by the singular value decomposition (SVD) technique. It is concluded that the SRIF filtering and smoothing algorithms are efficient and numerically stable for well-conditioned systems. The use of Bierman's ESL simplifies the task of maintaining the orbit determination software by providing efficient, tested filtering tools. For solving a large well-conditioned system (rank higher than 120), SRIF is approximately four times faster than SVD; however, for solving an ill-conditioned system, SVD is recommended.

Wang, Tseng-Chan↗

NASA NTRS1989

Image processing enhancement of high-resolution TEM micrographs of nanometer-size metal particles

The high-resolution TEM detectability of lattice fringes from metal particles supported on substrates is impeded by the substrate itself. Single value decomposition (SVD) and Fourier filtering (FFT) methods were applied to standard high resolution micrographs to enhance lattice resolution from particles as well as from crystalline substrates. SVD produced good results for one direction of fringes, and it can be implemented as a real-time process. Fourier methods are independent of azimuthal directions and allow separation of particle lattice planes from those pertaining to the substrate, which makes it feasible to detect possible substrate distortions produced by the supported particle. This method, on the other hand, is more elaborate, requires more computer time than SVD and is, therefore, less likely to be used in real-time image processing applications.

Artal, P.↗

NASA NTRS1990

Improved solution for system identification equations by Epsilon-Decomposition

Matrix eigenvalue theory is used to examine the source of ill-conditioning in linear algebraic equations. This approach highlights the crucial role played by the zero and near-zero eigenvalues and corresponding eigenvectors of poorly conditioned systems. Insight gained from this approach is used to significantly improve a recently developed solution procedure called Epsilon-Decomposition (E-D). E-D is an efficient alternative to Singular Value Decomposition (SVD) for ill-conditioned systems arising in parameter estimation and system identification studies. The efficiency of the improved E-D over SVD resides in the need to only obtain the zero and near-zero eigenvalues of the coefficient matrix as opposed to all of its eigenvalues and vectors (as required by SVD). Thus, the efficiency of E-D is significant for large matrices with small rank deficiency.

Ojalvo, Irving U.↗

NASA NTRS1998

Microwave Imaging on Metal Objects

This final report for the project discusses the attempts to model, using different methods, microwave image reconstruction. Maximum Entropy Method was not successful. Attempts to use Singular Value Decomposition (SVD) got some good results after initial failure. SVD is based upon a theory of linear algebra, to the effect that any M X N Matrix A whose number of rows M is greater than or equal to its number of columns, N can be written as the product of an M X N column-orthogonal matrix U, an N X N diagonal Matrix, W, with m positive or zero elements (the singular values) and the transposition of an N X N orthogonal matrix V. In microwave imaging, the scattered fields can be expressed by the induced current distribution. The SVD method required more contiguous computer memory than was available. Work was also done on the Conjugate Gradient Method (CGM), which didn't work well when tried earlier. It was found that separation of the imaginary part and the real part during calculation may work. This work was considered incomplete as of the end of the grant period.

Tolliver, C. L.↗

NASA NTRS2004

Trend and Variability of China Precipitation in Spring and Summer: Linkage to Sea Surface Temperatures

Observational records in the past 50 years show an upward trend of boreal-summer precipitation over central eastern China and a downward trend over northern China. During boreal spring, the trend is upward over southeastern China and downward over central eastern China. This study explores the forcing mechanism of these trends in association with the global sea-surface temperature (SST) variations on the interannual and inter-decadal timescales. Results based on Singular Value Decomposition analyses (SVD) show that the interannual variability of China precipitation in boreal spring and summer can be well defined by two centers of actions for each season, which are co-varying with two interannual modes of SSTs. The first SVD modes of precipitation in spring and summer, which are centered in southeastern China and northern China, respectively, are linked to an ENSO-like mode of SSTs. The second SVD modes of precipitation in both seasons are confined to central eastern China, and are primarily linked to SST variations over the warm pool and Indian Ocean. Features of the anomalous 850-hPa winds and 700-Wa geopotential height corresponding to these modes support a physical mechanism that explains the causal links between the modal variations of precipitation and SSTs. On the decadal and longer timescale, similar causal links are found between the same modes of precipitation and SSTs, except for the case of springtime precipitation over central eastern China. For this case, while the interannual mode of precipitation is positively correlated with the interannual variations of SSTs over the warm pool and Indian Ocean; the inter-decadal mode is negatively correlated with a different SST mode, the North Pacific mode. The later is responsible for the observed downward trend of springtime precipitation over central eastern China. For all other cases, both the interannual and inter-decadal variations of precipitation can be explained by the same mode of SSTs. The upward trend of springtime precipitation over southeastern China and downward trend of summertime precipitation over northern China are attributable to the warming trend of the ENSO-like mode. The recent frequent summertime floods over central eastern China are linked to the warming trend of SSTs over the warm pool and Indian Ocean.

Yang, Fanglin↗

NASA NTRS2005

A Survey of Singular Value Decomposition Methods and Performance Comparison of Some Available Serial Codes

This contractor report describes a performance comparison of available alternative complete Singular Value Decomposition (SVD) methods and implementations which are suitable for incorporation into point spread function deconvolution algorithms. The report also presents a survey of alternative algorithms, including partial SVD's special case SVD's, and others developed for concurrent processing systems.

Plassman, Gerald E.↗