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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Exploration with Scalable Gaussian Process Reinforcement Learning

Exploration is a challenging problem in reinforcement learning (RL), especially in environments with sparse rewards. Quantifying and utilizing the parametric uncertainty has been shown to be paramount for successful exploration [Osband et al., 2018]. Bayesian, or approximately Bayesian, methods present a principled means of estimating the parametric uncertainty in RL problems. Gaussian processes, nonparametric Bayesian models, are often impractical due to poor scalability and computational bottlenecks. We introduce a scalable Gaussian process RL (GPRL) method which directly induces sparsity in the covariance matrix to facilitate faster computation. This is a departure from previous GPRL methods which instead rely on data reduction and subsampling. We compare various covariance-based exploration techniques (Thompson sampling, upper confidence bound, and probabilistic maximum variance) which leverage our scalable GP framework in sparse reward environments. Finally, we show favorable comparison against the bootstrapped deep Q-Network.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2020

Provable Convergence of Plug-and-Play Priors With MMSE Denoisers

Plug-and-play priors (PnP) is a methodology for regularized image reconstruction that specifies the prior through an image denoiser. While PnP algorithms are well understood for denoisers performing maximum a posteriori probability (MAP) estimation, they have not been analyzed for the minimum mean squared error (MMSE) denoisers. Here we address this gap by establishing the first theoretical convergence result for the iterative shrinkage/thresholding algorithm (ISTA) variant of PnP for MMSE denoisers. We show that the iterates produced by PnP-ISTA with an MMSE denoiser converge to a stationary point of some global cost function. We validate our analysis on sparse signal recovery in compressive sensing by comparing two types of denoisers, namely the exact MMSE denoiser and the approximate MMSE denoiser obtained by training a deep neural net.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1983

Some constraints on the color-magnitude diagram of giants in the galactic spheroid

The color-magnitude diagram of giants in the Galactic spheroid is shown to be important in determining the number-color histogram of stars brighter than B = 19 mag. This result is demonstrated by comparing a standard Galaxy model with observations of 391 stars in a field in the direction of Aquarius (l = 36.5 deg, b = -51.1 deg). More than 80 percent of the spheroid stars and 40 percent of all stars in this magnitude range and direction are predicted to be giants. At most, a few percent of the spheroid stars in the current sample can lie on the main sequence bluer than the turn-off onto the giant branch near B - V approximately 0.4. The available observations suggest that the blue tip of the horizontal branch of the spheroid must be sparsely populated about a factor of 10 less than would be expected if the color-magnitude diagram of the spheroid were the same as diagrams for any of the globular clusters M3, M13, or M92. The total dispersion in colors (measurement errors and intrinsic dispersion) has a standard deviation in B - V color that is less than 0.2 mag.

Bahcall, J. N.↗
NASA NTRS1981

Electromagnetic backscattering from a sparse distribution of lossy dielectric scatterers

Electromagnetic backscattering from a sparse distribution of lossy dielectric particles having random orientation and position is studied. The paper begins by using the Foldy approximation to find an equation for the mean field. From this equation, an effective permittivity for the scattering medium is obtained. The correlation of the scattered field is found by employing the distorted Born approximation, i.e., particles embedded in the effective medium are assumed to be single scatterers. The above method is then used to find the backscattering coefficients from a leaf canopy. The leaf canopy is modeled by a half space of dielectric discs that are small in comparison to a wavelength. Numerical results show that the depolarized cross section is a sensitive function of leaf inclination angle statistics.

Lang, R. H.↗
NASA NTRS1990

A review of reduced Navier-Stokes computations for compressible viscous flows

A reduced form of the Navier-Stokes equations, defined by a single composite of the Euler, boundary layer, and triple deck approximations, is considered for the computation of viscous interacting flows. Global pressure or pseudopotential relaxation methods are integrated with coupled sparse matrix direct solvers or coupled strongly implicit ILU algorithms to efficiently capture sharp shocks and regions of recirculation. Solutions are obtained for a variety of 2D and 3D geometries and for Mach numbers (M) spanning the range from incompressible (M = 0) to supersonic (M = 6) flow.

Rubin, S. G.↗
NASA NTRS2004

Saturn's Rings, the Yarkovsky Effects, and the Ring of Fire

The dimensions of Saturn's A and B rings may be determined by the seasonal Yarkovsky effect and the Yarkovsky-Schach effect; the two effects confine the rings between approximately 1.68 and approximately 2.23 Saturn radii, in reasonable agreement with the observed values of 1.525 and 2.267. The C ring may be sparsely populated because its particles are transients on their way to Saturn; the infall may create a luminous Ring of Fire around Saturn's equator. The ring system may be young: in the past heat flow from Saturn's interior much above its present value would not permit rings to exist.

Rubincam, David Parry↗
NASA NTRS2019

Electromagnetic Scattering by Discrete Random Media. II: The Coherent Field

The computation of the coherent field in the case of a plane electromagnetic wave obliquely incident on a discrete random layer with non-scattering boundaries is addressed. For dense media, the analysis is based on a special-form solution for the conditional configuration-averaged exciting field coefficients, and is restricted to the computation of the so-called zeroth-order fields without a special treatment of the boundary regions. In this setting, we calculate the coherent fields reflected and transmitted by the layer, and the coherent field inside the layer. We found that these fields are analytically equivalent to plane electromagnetic waves, and investigated the fulfillment of the boundary conditions for the electric fields at the layer interfaces. The results are then particularized to the cases of normal incidence and a semi-infinite discrete random medium. For sparsely distributed particles, we present a self-consistent derivation of the coherent field and discuss the Twersky and Foldy approximations.

Adrian Doicu↗
NASA NTRS2012

G-LiHT: Goddard's LiDAR, Hyperspectral and Thermal Airborne Imager

Scientists at NASA's Goddard Space Flight Center have developed an ultra-portable, low-cost, multi-sensor remote sensing system for studying the form and function of terrestrial ecosystems. G-LiHT integrates two LIDARs, a 905 nanometer single beam profiler and 1550 nm scanner, with a narrowband (1.5 nanometers) VNIR imaging spectrometer and a broadband (8-14 micrometers) thermal imager. The small footprint (approximately 12 centimeters) LIDAR data and approximately 1 meter ground resolution imagery are advantageous for high resolution applications such as the delineation of canopy crowns, characterization of canopy gaps, and the identification of sparse, low-stature vegetation, which is difficult to detect from space-based instruments and large-footprint LiDAR. The hyperspectral and thermal imagery can be used to characterize species composition, variations in biophysical variables (e.g., photosynthetic pigments), surface temperature, and responses to environmental stressors (e.g., heat, moisture loss). Additionally, the combination of LIDAR optical, and thermal data from G-LiHT is being used to assess forest health by sensing differences in foliage density, photosynthetic pigments, and transpiration. Low operating costs (approximately $1 ha) have allowed us to evaluate seasonal differences in LiDAR, passive optical and thermal data, which provides insight into year-round observations from space. Canopy characteristics and tree allometry (e.g., crown height:width, canopy:ground reflectance) derived from G-LiHT data are being used to generate realistic scenes for radiative transfer models, which in turn are being used to improve instrument design and ensure continuity between LiDAR instruments. G-LiHT has been installed and tested in aircraft with fuselage viewports and in a custom wing-mounted pod that allows G-LiHT to be flown on any Cessna 206, a common aircraft in use throughout the world. G-LiHT is currently being used for forest biomass and growth estimation in the CONUS and Mexico in support of NASA's Carbon Monitoring System (CMS) and AMIGA-Carb (AMerican Icesat Glas Assessment of Carbon). For NASA's CMS, wall-to-wall G-LiHT data have been acquired over intensive study sites with historic LiDAR datasets, dense inventory data, stem maps and flux tower observations. For AMIGA-Carb, G-LiHT transects have been acquired over ICESat tracks and USDA-FS inventory plots throughout the CONUS, and similar data will be acquired in Mexico during 2013. This talk will highlight recent science results from continental-scale transects landscape-scale deployments of G-LiHT, as well as seasonal forest dynamics from repeat pass G-LiHT acquisitions.

Cook, Bruce↗
NASA NTRS2012

Can Asian Dust Trigger Phytoplankton Blooms in the Oligotrophic Northern South China Sea?

Satellite data estimate a high dust deposition flux (approximately 18 g m(exp-2 a(exp-1) into the northern South China Sea (SCS). However, observational evidence concerning any biological response to dust fertilization is sparse. In this study, we combined long-term aerosol and chlorophyll-a (Chl-a) measurements from satellite sensors (MODIS and SeaWiFS) with a 16-year record of dust events from surface PM10 observations to investigate dust transport, flux, and the changes in Chl-a concentration over the northern SCS. Our result revealed that readily identifiable strong dust events over this region, although relatively rare (6 cases since 1994) and accounting for only a small proportion of the total dust deposition (approximately 0.28 g m(exp-2 a(exp-1), do occur and could significantly enhance phytoplankton blooms. Following such events, the Chl-a concentration increased up to 4-fold, and generally doubled the springtime background value (0.15 mg m(exp-3). We suggest these heavy dust events contain readily bioavailable iron and enhance the phytoplankton growth in the oligotrophic northern SCS.

northern South China sea↗
DOE OSTI2025

Real-Time Operator Evolution in Two and Three Dimensions via Sparse Pauli Dynamics

We study real-time operator evolution using sparse Pauli dynamics, a recently developed method for simulating expectation values of quantum circuits. On the examples of energy and charge diffusion in one-dimensional (1D) spin chains and sudden quench dynamics in the 2D transverse-field Ising model, it is shown that this approach can compete with state-of-the-art tensor network methods. We further demonstrate the flexibility of the approach by studying quench dynamics in the 3D transverse-field Ising model that is highly challenging for tensor network methods. For the simulation of expectation value dynamics starting in a computational basis state, we introduce an extension of sparse Pauli dynamics that truncates the growing sum of Pauli operators by discarding terms with a large number of X and Y matrices. This is validated by our 2D and 3D simulations. Finally, we argue that sparse Pauli dynamics is not only capable of converging challenging observables to high accuracy, but can also serve as a reliable approximate approach even when given only limited computational resources. Published by the American Physical Society 2025

Begušić, Tomislav (ORCID:0000000279424134)↗
DOE OSTI2025

powersqueeze

powersqueeze (psqz) is a truncated power iteration library intended for high-performance computing platforms. psqz efficiently produces low-dimensional, linear measurements of graph matrix spectra by combining classical power iteration with sparse Johnson-Lindenstrauss transforms. psqz is intended to produce high-quality, fast, data-oblivious low-dimensional representations of high-dimensional sparse data such as graphs and term-document matrices. psqz is intended to replace similar workflows that depend on directly approximating a truncated eigendecomposition (e.g., the first step of spectral clustering), which is a much more expensive operation.

Priest, BenjaminW [Lawrence Livermore National Lab↗
NASA NTRS1983

Preconditioners for the spectral multigrid method

The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problems preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented.

Phillips, T. N.↗
NASA NTRS1986

Preconditioners for the spectral multigrid method

The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problem preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented.

Phillips, T. N.↗
NASA NTRS1994

Discretized energy minimization in a wave guide with point sources

An anti-noise problem on a finite time interval is solved by minimization of a quadratic functional on the Hilbert space of square integrable controls. To this end, the one-dimensional wave equation with point sources and pointwise reflecting boundary conditions is decomposed into a system for the two propagating components of waves. Wellposedness of this system is proved for a class of data that includes piecewise linear initial conditions and piecewise constant forcing functions. It is shown that for such data the optimal piecewise constant control is the solution of a sparse linear system. Methods for its computational treatment are presented as well as examples of their applicability. The convergence of discrete approximations to the general optimization problem is demonstrated by finite element methods.

Propst, G.↗
NASA NTRS1995

Validation of Global Climatologies of Trace Gases Using NASA Global Tropospheric Experiment (GTE) Data

Methane is an important trace gas because it is a greenhouse gas that affects the oxidative capacity of the atmosphere. It is produced from biological and anthropogenic sources, and is increasing globally at a rate of approximately 0.6% per year [Climate Change 1992, IPCC]. By using National Oceanic and Atmospheric Administration/Climate Monitoring and Diagnostics Laboratory (NOAA/CMDL) ground station data, a global climatology of methane values was produced. Unfortunately, because the NOAA/CMDL ground stations are so sparse, the global climatology is low resolution. In order to compensate for this low resolution data, it was compared to in-situ flight data obtained from the NASA Global Tropospheric Experiment (GTE). The smoothed ground station data correlated well with the flight data. Thus, for the first time it is shown that the smoothing process used to make global contours of methane using the ground stations is a plausible way to approximate global atmospheric concentrations of the gas. These verified climatologies can be used for testing large-scale models of chemical production, destruction, and transport. This project develops the groundwork for further research in building global climatologies from sparse ground station data and studying the transport and distribution of trace gases.

Courchaine, Brian↗
NASA NTRS1983

Progress on a generalized coordinates tensor product finite element 3DPNS algorithm for subsonic

A generalized coordinates form of the penalty finite element algorithm for the 3-dimensional parabolic Navier-Stokes equations for turbulent subsonic flows was derived. This algorithm formulation requires only three distinct hypermatrices and is applicable using any boundary fitted coordinate transformation procedure. The tensor matrix product approximation to the Jacobian of the Newton linear algebra matrix statement was also derived. Tne Newton algorithm was restructured to replace large sparse matrix solution procedures with grid sweeping using alpha-block tridiagonal matrices, where alpha equals the number of dependent variables. Numerical experiments were conducted and the resultant data gives guidance on potentially preferred tensor product constructions for the penalty finite element 3DPNS algorithm.

Baker, A. J.↗
NASA NTRS1986

Canopy reflectance modeling in a tropical wooded grassland

Geometric/optical canopy reflectance modeling and spatial/spectral pattern recognition is used to study the form and structure of savanna in West Africa. An invertible plant canopy reflectance model is tested for its ability to estimate the amount of woody vegetation from remotely sensed data in areas of sparsely wooded grassland. Dry woodlands and wooded grasslands, commonly referred to as savannas, are important ecologically and economically in Africa, and cover approximately forty percent of the continent by some estimates. The Sahel and Sudan savannas make up the important and sensitive transition zone between the tropical forests and the arid Sahara region. The depletion of woody cover, used for fodder and fuel in these regions, has become a very severe problem for the people living there. LANDSAT Thematic Mapper (TM) data is used to stratify woodland and wooded grassland into areas of relatively homogeneous canopy cover, and then an invertible forest canopy reflectance model is applied to estimate directly the height and spacing of the trees in the stands. Because height and spacing are proportional to biomass in some cases, a successful application of the segmentation/modeling techniques will allow direct estimation of tree biomass, as well as cover density, over significant areas of these valuable and sensitive ecosystems. The model being tested in sites in two different bioclimatic zones in Mali, West Africa, will be used for testing the canopy model. Sudanian zone crop/woodland test sites were located in the Region of Segou, Mali.

Simonett, David↗