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At least 1,387 records · Page 77
All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Assessment of Biases in MODIS Surface Reflectance Due to Lambertian Approximation

Using MODIS data and the AERONET-based Surface Reflectance Validation Network (ASRVN), this work studies errors of MODIS atmospheric correction caused by the Lambertian approximation. On one hand, this approximation greatly simplifies the radiative transfer model, reduces the size of the look-up tables, and makes operational algorithm faster. On the other hand, uncompensated atmospheric scattering caused by Lambertian model systematically biases the results. For example, for a typical bowl-shaped bidirectional reflectance distribution function (BRDF), the derived reflectance is underestimated at high solar or view zenith angles, where BRDF is high, and is overestimated at low zenith angles where BRDF is low. The magnitude of biases grows with the amount of scattering in the atmosphere, i.e., at shorter wavelengths and at higher aerosol concentration. The slope of regression of Lambertian surface reflectance vs. ASRVN bidirectional reflectance factor (BRF) is about 0.85 in the red and 0.6 in the green bands. This error propagates into the MODIS BRDF/albedo algorithm, slightly reducing the magnitude of overall reflectance and anisotropy of BRDF. This results in a small negative bias of spectral surface albedo. An assessment for the GSFC (Greenbelt, USA) validation site shows the albedo reduction by 0.004 in the near infrared, 0.005 in the red, and 0.008 in the green MODIS bands.

Wang, Yujie↗
NASA NTRS2019

Improving Satellite Global Chlorophyll a [alpha] Data Products Through Algorithm Refinement and Data Recovery

A recently developed algorithm to estimate surface ocean chlorophyll a concentrations (Chl in milligrams per cubic meter), namely, the ocean color index (OCI) algorithm, has been adopted by the U.S. National Aeronautics and Space Administration to apply to all satellite ocean color sensors to produce global Chl maps. The algorithm is a hybrid between a band‐difference color index algorithm for low‐Chl waters and the traditional band‐ratio algorithms (OCx) for higher‐Chl waters. In this study, the OCI algorithm is revisited for its algorithm coefficients and for its algorithm transition between color index and OCx using a merged data set of high‐performance liquid chromatography and fluorometric Chl. Results suggest that the new OCI algorithm (OCI2) leads to lower Chl estimates than the original OCI (OCI1) for Chl less than 0.05 milligrams per cubic meter, but smoother algorithm transition for Chl between 0.25 and 0.40 milligrams per cubic meter. Evaluation using in situ data suggests that similar to OCI1, OCI2 has significantly improved image quality and cross‐sensor consistency between SeaWiFS (Sea-viewing Wide Field-of-view Sensor), MODISA (Moderate Resolution Imaging Spectroradiometer on Aqua), and VIIRS (Visible Infrared Imaging Radiometer Suite) over the OCx algorithms for oligotrophic oceans. Mean cross‐sensor difference in monthly Chl data products over global oligotrophic oceans reduced from approximately 10 percent for OCx to 1-2 percent for OCI2. More importantly, data statistics suggest that the current straylight masking scheme used to generate global Chl maps can be relaxed from 7 by 5 to 3 by 3 pixels without losing data quality in either Chl or spectral remote sensing reflectance (R (sub rs) by lambda (sensor wavelength), per steradian (sr (sup −1)) for not just oligotrophic oceans but also more productive waters. Such a relaxed masking scheme yields an average relative increase of 39 percent in data quantity for global oceans, thus making it possible to reduce data product uncertainties and fill data gaps.

Hu, Chuanmin↗
NASA NTRSDate not supplied

Modeling the Effective Elasticity of Anisotropic Porous Materials

The development and optimization of composite materials designed for thermal protection of NASA’s spacecraft require understanding their physical response to high-enthalpy environments. To predict their macro-scale properties and behavior, high-fidelity 3D simulations are performed at the microscale on realistic representations of these composites. The digital microstructures are generated either synthetically or through X-ray micro-computed tomography reconstructions. One of the main challenges in the prediction of the structural response of heatshield materials is the computation of the effective elasticity of the fibrous composite, as well as the understanding of the deformation and stresses generated at the microscale. These are driven by the fiber layout within the microstructure and the distribution of the infused matrix. In this effort, the micro-mechanical linear elastic behavior of fibrous ablators is modeled using a numerical method based on the Multi-Point Stress Approximation (MPSA) finite volume scheme, a generalization of the more commonly used Multi-Point Flux Approximation (MPFA) that was presented at the 10th Ablation Workshop. To predict the behavior of fibrous and woven architectures, algorithms that compute the local fiber orientation are used. The implementation of the MPSA was verified using analytical solutions, engineering test cases, and compared against legacy Finite Element Analysis (FEA) software. The stress analysis models were then applied to real geometries used by NASA in thermal protection systems such as fibrous preforms and woven materials and the results were compared to experimental data.

Elasticity↗
NASA NTRS1993

Simulated retrieval of land surface parameters using multichannel satellite microwave radiometry

The current global change research emphasis on understanding water and energy fluxes at the land-atmosphere interface provided renewed interest in using passive microwave satellite data for land studies. Radiative transfer models of microwave emission and scattering in the soil-vegetation-atmosphere column, though still in the process of development, can be used to estimate the accuracies with which land surface parameters can be derived from satellite data. These parameters include surface soil moisture, surface temperature, vegetation water content, and atmospheric water content. A microwave radiative transfer model is used to develop linear and nonlinear versions of a multichannel retrieval algorithm to simulate retrievals of the surface and atmospheric parameters. These simulations include the effect of additive noise, and examine the effects of nonlinearities in the radiative transfer models. However, effects of spatial heterogeneity are not considered. Satellite data to which the retrieval algorithms may be applied include the SSMR and SSM/I, and in future will include the Multifrequency Imaging Microwave Radiometer (MIMR) to be launched as part of the Earth Observing System (EOS). The Scanning Multichannel Microwave Radiometer (SMMR) on the Nimbus-7 satellite provided data from 1978 to 1987 at five microwave frequencies between 6.6 and 37 GHz. The series of Special Sensor Microwave/Imager (SSM/I) instruments launched on the DMSP satellites provide data from 1987 to the present at four frequencies between 19.35 and 8.5 GHz. Spatial resolutions of the data range from approximately 12 to 120 km depending on the frequency. Examples using data from these sensors are shown to indicate the results of applying retrieval algorithms based on model simulations to real data.

Njoku, Eni G.↗
DOE OSTI2024

Gradient Coding With Iterative Block Leverage Score Sampling

Gradient coding is a method for mitigating straggling servers in a centralized computing network that uses erasure-coding techniques to distributively carry out first-order optimization methods. Randomized numerical linear algebra uses randomization to develop improved algorithms for large-scale linear algebra computations. In this study, we propose a method for distributed optimization that combines gradient coding and randomized numerical linear algebra. The proposed method uses a randomized ℓ 2 -subspace embedding and a gradient coding technique to distribute blocks of data to the computational nodes of a centralized network, and at each iteration the central server only requires a small number of computations to obtain the steepest descent update. The novelty of our approach is that the data is replicated according to importance scores, called block leverage scores, in contrast to most gradient coding approaches that uniformly replicate the data blocks. Furthermore, we do not require a decoding step at each iteration, avoiding a bottleneck in previous gradient coding schemes. We show that our approach results in a valid ℓ 2 -subspace embedding, and that our resulting approximation converges to the optimal solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Variational Monte Carlo Calculations of A ≤ 4 Nuclei with an Artificial Neural-Network Correlator Ansatz

Here, the complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry where nonperturbative interactions are prominent. Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems. In this work we introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei, and approximately solve the nuclear many-body Schrodinger equation. Using efficient stochastic sampling and optimization schemes, our approach extends pioneering applications of ANNs in the field, which present exponentially scaling algorithmic complexity. We compute the binding energies and point-nucleon densities of A ≤ 4 nuclei as emerging from a leading-order pionless effective field theory Hamiltonian. We successfully benchmark the ANN wave function against more conventional parametrizations based on two- and three-body Jastrow functions, and virtually exact Green's function Monte Carlo results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2002

Distant Cluster Hunting: A Comparison of X-Ray and Optical Cluster Detection Techniques and Catalogs from the ROSAT Optical X-Ray Survey - II

We present and analyze the optical and X-ray catalogs of moderate-redshift cluster candidates from the ROSA TOptical X-Ray Survey, or ROXS. The survey covers the sky area contained in the fields of view of 23 deep archival ROSA T PSPC pointings, 4.8 square degrees. The cross-correlated cluster catalogs were con- structed by comparing two independent catalogs extracted from the optical and X-ray bandpasses, using a matched-filter technique for the optical data and a wavelet technique for the X-ray data. We cross-identified cluster candidates in each catalog. As reported in Paper 1, the matched-filter technique found optical counter- parts for at least 60% (26 out of 43) of the X-ray cluster candidates; the estimated redshifts from the matched filter algorithm agree with at least 7 of 1 1 spectroscopic confirmations (Az 5 0.10). The matched filter technique. with an imaging sensitivity of ml N 23, identified approximately 3 times the number of candidates (155 candidates, 142 with a detection confidence >3 u) found in the X-ray survey of nearly the same area. There are 57 X-ray candidates, 43 of which are unobscured by scattered light or bright stars in the optical images. Twenty-six of these have fairly secure optical counterparts. We find that the matched filter algorithm, when applied to images with galaxy flux sensitivities of mI N 23, is fairly well-matched to discovering z 5 1 clusters detected by wavelets in ROSAT PSPC exposures of 8000-60,000 s. The difference in the spurious fractions between the optical and X-ray (30%) and IO%, respectively) cannot account for the difference in source number. In Paper I, we compared the optical and X-ray cluster luminosity functions and we found that the luminosity functions are consistent if the relationship between X-ray and optical luminosities is steep (Lx o( L&f). Here, in Paper 11, we present the cluster catalogs and a numerical simulation of the ROXS. We also present color-magnitude plots for several of the cluster candidates, and examine the prominence of the red sequence in each. We find that the X-ray clusters in our survey do not all have a prominent red sequence. We conclude that while the red sequence may be a distinct feature in the color-magnitude plots for virialized massive clusters, it may be less distinct in lower mass clusters of galaxies at even moderate redshifts. Multiple, complementary methods of selecting and defining clusters may be essential, particularly at high redshift where all methods start to run into completeness limits, incomplete understanding of physical evolution, and projection effects.

Donahue, Megan↗
NASA NTRS1978

ORACLS: A system for linear-quadratic-Gaussian control law design

A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

Armstrong, E. S.↗
NASA NTRS1992

Rain compensation algorithm for ACTS mobile terminal

The initial advanced communication technology satellite (ACTS) mobile terminal (AMT) demonstrations will involve two-way communications between the high-bit-rate link evaluation terminal (HBR-LET), which is a fixed terminal (FT), and a van-housed mobile terminal (MT). The HBR-LET has the capability of adjusting its transmitted uplink power over an approximately 10-dB range to compensate for forward uplink rain attenuation. However, because of size and weight limitations, the MT cannot use power control as a rain compensation technique. Consequently, the AMT rain compensation algorithm (RCA) is based on a formula for varying the transmitted data rate in either direction to maintain link performance within acceptable limits. The objective of the AMT RCA is to ensure reliable operation in both the forward and return directions despite the possibility of uplink or downlink fading due to rain events in the vicinity of the FT or MT. In particular, the RCA must maintain at least a 3-dB link margin at the highest possible transmission rate (AMT can operate at 9.6, 4.8, or 2.4 kb/s) permitted by the prevailing channel conditions. The 3-dB minimum link margin is a system design safety factor to accommodate conceivable implementation losses.

Levitt, Barry K.↗
DOE OSTI2025

Performance Improvements Through Advanced PV Backtracking on Uneven Terrain

The climatic sensitivity of new terrain-aware backtracking algorithms is evaluated across 800 locations in the continental USA on a representative synthetic rolling terrain. We find that a global optimization approach to backtracking results in climate-specific annual energy gains of 2.4%–3.2% relative to a traditional backtracking algorithm baseline. We identify a strong logarithmic correlation between local diffuse fraction and yield improvement, and highlight the effect of seasonal precipitation on performance gains. We also find that a backtracking approach, which approximates the terrain as constant, does not offer significant annual energy gains over the baseline on the synthetic terrain. Our findings suggest that specific yield from backtracking in the USA can be improved by as much as 88 kWh/kW by considering terrain when selecting a backtracking algorithm.

Backtracking↗
DOE OSTI2023

Online Adaptive Algorithm for Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method

Here in this research, we propose an online basis enrichment strategy within the framework of a recently developed constraint energy minimizing generalized multiscale discontinuous Galerkin method. Combining the technique of oversampling, one makes use of the information of the current residuals to adaptively construct basis functions in the online stage to reduce the error of multiscale approximation. A complete analysis of the method is presented, which shows the proposed online enrichment leads to a fast convergence from multiscale approximation to the fine-scale solution. The error reduction can be made sufficiently large by suitably selecting oversampling regions and the number of oversampling layers. Further, the convergence rate of the enrichment algorithm depends on a factor of exponential decay regarding the number of oversampling layers and a user-defined parameter. Numerical results are provided to demonstrate the effectiveness and efficiency of the proposed online adaptive algorithm.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1996

Stochastic Filtering of Rain Profiles Using Radar, Surface-Referenced Radar, or Combined Radar-Radiometer Measurements

This paper describes a computationally efficient nearly optimal Bayesian algorithm to estimate rain (and drop size distribution) profiles, given a radar reflectivity profile at a single attenuating wavelength. In addition to estimating the averages of all the mutually ambiguous combinations of rain parameters that can produce the data observed, the approach also calculates the n-ns uncertainty in its estimates (this uncertainty thus quantifies "the amount of ambiguity" in the "solution"). The paper also describes a more general approach that can make estimates based on a radar reflectivity profile together with an approximate measurement of the path-integrated attenuation, or a radar reflectivity profile and a set of passive microwave brightness temperatures. This more general "combined" algorithm is currently being adapted for the Tropical Rainfall Measuring Mission.

Haddad, Ziad S.↗
DOE OSTI2022

Performance Evaluations of Noisy Approximate Quantum Fourier Arithmetic

The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route towards a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor’s algorithm, weighted sum optimization problems in data processing and machine learning and quantum algorithms requiring inner products. We carry out performance evaluations of these implementations based on IBM’s superconducting qubit architecture using different compatible noise models. We isolate the sensitivity of the component quantum circuits on both one-/two-qubit gate error rates, and the number of the arithmetic operands’ superposed integer states. We analyze performance, and identify the most effective approximation depths for quantum add and quantum multiply within the given context. We observe significant dependency of the optimal approximation depth on the degree of machine noise and the number of superposed states in certain performance regimes. Finally, we elaborate on the algorithmic challenges - relevant to signed, unsigned, modular and non-modular versions - that could also be applied to current implementations of QFT-based subtraction, division, exponentiation, and their potential tensor extensions. Here, we analyze performance trends in our results and speculate on possible future development within this computational paradigm.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1980

Nonreflecting far-field boundary conditions for unsteady transonic flow computation

The approximate nonreflecting far-field boundary condition, as proposed by Engquist and Majda, is implemented in the computer code LTRAN2. This code solves the implicit finite-difference representation of the small disturbance equations for unsteady transonic flows about airfoils. The nonreflecting boundary condition and the description of the algorithm for implementing these conditions in LTRAN2 are discussed. Various cases are computed and compared with results from the older, more conventional procedures. One concludes that the nonreflecting far-field boundary approximation allows the far-field boundary to be located closer to the airfoil; this permits a decrease in the computer time required to obtain the solution through the use of fewer mesh points.

Kwak, D.↗
DOE OSTI2021

An infeasible-start framework for convex quadratic optimization, with application to constraint-reduced interior-point and other methods

A framework is proposed for solving general convex quadratic programs (CQPs) from an infeasible starting point by invoking an existing feasible-start algorithm tailored for inequality-constrained CQPs. The central tool is an exact penalty function scheme equipped with a penalty-parameter updating rule. The feasible-start algorithm merely has to satisfy certain general requirements, and so is the updating rule. Under mild assumptions, the framework is proved to converge on CQPs with both inequality and equality constraints and, at a negligible additional cost per iteration, produces an infeasibility certificate, together with a feasible point for an (approximately) ℓ 1 -least relaxed feasible problem, when the given problem does not have a feasible solution. The framework is applied to a feasible-start constraint-reduced interior-point algorithm previously proved to be highly performant on problems with many more inequality constraints than variables (“imbalanced”). Numerical comparison with popular codes (OSQP, qpOASES, MOSEK) is reported on both randomly generated problems and support-vector machine classifier training problems. The results show that the former typically outperforms the latter on imbalanced problems. Finally, application of the proposed infeasible-start framework to other feasible-start algorithms is briefly considered, and is tested on a simplex iteration.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1981

Nonreflecting Far-Field Boundary Conditions for Unsteady Transonic Flow Computation

The approximate nonreflecting far-field boundary condition, as proposed by Engquisi and Majda, is implemented In the computer code LTRAN2. This code solves the Implicit finite-difference representation of the small-disturbance equations for unsteady transonic flows about airfoils. The nonreflecting boundary condition and the description of the algorithm for Implementing these conditions In LTRAN2 tire discussed. Various cases re computed and compared with results from the older, more conventional procedures. One concludes that the nonreflecting far-field boundary approximation allows the far-field boundary to be located closer to the airfoil; this permits a decrease in the computer lime required to obtain the solution through the use of fewer mesh points.

Kwak, D.↗
DOE OSTI2024

Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Nonlinear Matrix Approximation with Radial Basis Function Components

We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the scalar multiplication between individual vector elements. Even though the RBF functions are positive definite, the summation across components is not restricted to convex combinations and allows us to compute the decomposition for any real matrix that is not necessarily symmetric or positive definite. We formulate the problem of seeking such a decomposition as an optimization problem with a nonlinear and non-convex loss function. Several modern versions of the gradient descent method, including their scalable stochastic counterparts, are used to solve this problem. We provide extensive empirical evidence of the effectiveness of the RBF decomposition and that of the gradient-based fitting algorithm. While being conceptually motivated by singular value decomposition (SVD), our proposed nonlinear counterpart outperforms SVD by drastically reducing the memory required to approximate a data matrix with the same L2 error for a wide range of matrix types. For example, it leads to 2 to 6 times memory save for Gaussian noise, graph adjacency matrices, and kernel matrices. Moreover, this proximity-based decomposition can offer additional interpretability in applications that involve, e.g., capturing the inner low-dimensional structure of the data, retaining graph connectivity structure, and preserving the acutance of images.

Rebrova, Elizaveta↗