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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A Scalable Space-Time Domain Decomposition Approach for Solving Large Scale Nonlinear Regularized Inverse Ill Posed Problems in 4D Variational Data Assimilation

We address the development of innovative algorithms designed to solve the strong-constraint Four Dimensional Variational Data Assimilation (4DVar DA) problems in large scale applications. We present a space-time decomposition approach which employs the whole domain decomposition, i.e. both along the spacial and temporal direction in the overlapping case, and the partitioning of both the solution and the operator. Starting from the global functional defined on the entire domain, we get to a sort of regularized local functionals on the set of sub domains providing the order reduction of both the predictive and the Data Assimilation models. The algorithm convergence is developed. Performance in terms of reduction of time complexity and algorithmic scalability is discussed on the Shallow Water Equations on the sphere. The number of state variables in the model, the number of observations in an assimilation cycle, as well as numerical parameters as the discretization step in time and in space domain are defined on the basis of discretization grid used by data available at repository Ocean Synthesis/Reanalysis Directory of Hamburg University.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Biomass char gasification kinetic rates compared to data, including ash effects

This investigation provides both experimental and theoretical analyses of biomass char gasification kinetics over 1150–1350 °C in the environment of CO 2 , H 2 O and combinations of these reactants. The experimental data include continuous measurements of particle mass, external and internal temperatures, shape, and size with periodic but not continuous measurements of char porosity, pore size distribution, and pore surface area. The model describes heterogeneous char gasification for poplar wood, corn stover and switchgrass in different shapes and industrially relevant sizes (12.5 mm and smaller). Nonlinear least-squares regression produces optimized power-law model parameters for global kinetics that describe biomass char gasification with respect to both CO 2 and H 2 O separately and in combination. A single set of kinetic parameters describes reaction rates for all three fuels. Model simulations agree with measured data at all stages of char conversion even though the observed mass loss rates change significantly with conversion. In conclusion, the change in rate with conversion depends strongly on ash content, and this investigation provides a simple and theoretically based reaction rate expression that includes the effect of inert ash occupying an increasing portion of the reactive surface with increased conversion.

09 BIOMASS FUELS↗
DOE OSTI2021

Quasi-periodic travelling gravity–capillary waves

We present a numerical study of spatially quasi-periodic travelling waves on the surface of an ideal fluid of infinite depth. This is a generalization of the classic Wilton ripple problem to the case when the ratio of wavenumbers satisfying the dispersion relation is irrational. We propose a conformal mapping formulation of the water wave equations that employs a quasi-periodic variant of the Hilbert transform to compute the normal velocity of the fluid from its velocity potential on the free surface. We develop a Fourier pseudo-spectral discretization of the travelling water wave equations in which one-dimensional quasi-periodic functions are represented by two-dimensional periodic functions on the torus. This leads to an overdetermined nonlinear least-squares problem that we solve using a variant of the Levenberg–Marquardt method. We investigate various properties of quasi-periodic travelling waves, including Fourier resonances, time evolution in conformal space on the torus, asymmetric wave crests, capillary wave patterns that change from one gravity wave trough to the next without repeating and the dependence of wave speed and surface tension on the amplitude parameters that describe a two-parameter family of waves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

NIR fluorescence lifetime macroscopic imaging with a time-gated SPAD camera

The performance of SwissSPAD2 (SS2), a large scale, widefield time-gated CMOS SPAD imager developed for fluorescence lifetime imaging, has recently been described in the context of visible range and fluorescence lifetime imaging microscopy (FLIM) of dyes with lifetimes in the 2.5 – 4 ns range. Here, we explore its capabilities in the NIR regime relevant for small animal imaging, where its sensitivity is lower and typical NIR fluorescent dye lifetimes are much shorter (1 ns or less). We carry out this study in a simple macroscopic imaging setup based on a compact NIR picosecond pulsed laser, an engineered diffuser-based illumination optics, and NIR optimized imaging lens suitable for well-plate or small animal imaging. Because laser repetition rates can vary between models, but the synchronization signal frequency accepted by SS2 is fixed to 20 MHz, we first checked that a simple frequency-division scheme enables data recording for different laser repetition rates. Next, we acquired data using different time gate widths, including gates with duration longer than the laser period, and analyzed the resulting data using both standard nonlinear least-square fit (NLSF) and phasor analysis. We show that the fixed synchronization rate and large gate widths characterizing SS2 (10 ns and over) are not an obstacle to accurately extracting lifetime in the 1 ns range and to distinguishing between close lifetimes. As a result, SS2 and similar very large gated SPAD imagers appear as a versatile alternative to other widefield time-resolved detectors for NIR fluorescence lifetime imaging, including preclinical molecular applications.

FLIM↗
DOE OSTI2021

Train Like a (Var)Pro: Efficient Training of Neural Networks with Variable Projection

Deep neural networks (DNNs) have achieved state-of-the-art performance across a variety of traditional machine learning tasks, e.g., speech recognition, image classification, and segmentation. The ability of DNNs to efficiently approximate high-dimensional functions has also motivated their use in scientific applications, e.g., to solve partial differential equations and to generate surrogate models. In this paper, we consider the supervised training of DNNs, which arises in many of the above applications. We focus on the central problem of optimizing the weights of the given DNN such that it accurately approximates the relation between observed input and target data. Devising effective solvers for this optimization problem is notoriously challenging due to the large number of weights, nonconvexity, data sparsity, and nontrivial choice of hyperparameters. To solve the optimization problem more efficiently, we propose the use of variable projection (VarPro), a method originally designed for separable nonlinear least-squares problems. Our main contribution is the Gauss--Newton VarPro method (GNvpro) that extends the reach of the VarPro idea to nonquadratic objective functions, most notably cross-entropy loss functions arising in classification. These extensions make GNvpro applicable to all training problems that involve a DNN whose last layer is an affine mapping, which is common in many state-of-the-art architectures. In our four numerical experiments from surrogate modeling, segmentation, and classification, GNvpro solves the optimization problem more efficiently than commonly used stochastic gradient descent (SGD) schemes. Finally, GNvpro finds solutions that generalize well, and in all but one example better than well-tuned SGD methods, to unseen data points.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A two-phase substrate model for enzymatic hydrolysis of lignocellulose: application to batch and continuous reactors

Abstract Background Enzymatic hydrolysis continues to have a significant projected production cost for the biological conversion of biomass to fuels and chemicals, motivating research into improved enzyme and reactor technologies in order to reduce enzyme usage and equipment costs. However, technology development is stymied by a lack of accurate and computationally accessible enzymatic-hydrolysis reaction models. Enzymatic deconstruction of cellulosic materials is an exceedingly complex physico-chemical process. Models which elucidate specific mechanisms of deconstruction are often too computationally intensive to be accessible in process or multi-physics simulations, and empirical models are often too inflexible to be effectively applied outside of their batch contexts. In this paper, we employ a phenomenological modeling approach to represent rate slowdown due to substrate structure (implemented as two substrate phases) and feedback inhibition, and apply the model to a continuous reactor system. Results A phenomenological model was developed in order to predict glucose and solids concentrations in batch and continuous enzymatic-hydrolysis reactors from which liquor is continuously removed by ultrafiltration. A series of batch experiments were performed, varying initial conditions (solids, enzyme, and sugar concentrations), and best-fit model parameters were determined using constrained nonlinear least-squares methods. The model achieved a good fit for overall sugar yield and insoluble solids concentration, as well as for the reduced rate of sugar production over time. Additionally, without refitting model coefficients, good quantitative agreement was observed between results from continuous enzymatic-hydrolysis experiments and model predictions. Finally, the sensitivity of the model to its parameters is explored and discussed. Conclusions Although the phenomena represented by the model correspond to behaviors that emerge from clusters of mechanisms, and hence a set of model coefficients are unique to the substrate and the enzyme system, the model is efficient to solve and may be applied to novel reactor schema and implemented in computational fluid dynamics (CFD) simulations. Hence, this modeling approach finds the right balance between model complexity and computational efficiency. These capabilities have broad application to reactor design, scale-up, and process optimization.

09 BIOMASS FUELS↗
DOE OSTI2021

Efficient ptychographic phase retrieval via a matrix-free Levenberg-Marquardt algorithm

The phase retrieval problem, where one aims to recover a complex-valued image from far-field intensity measurements, is a classic problem encountered in a range of imaging applications. Modern phase retrieval approaches usually rely on gradient descent methods in a nonlinear minimization framework. Calculating closed-form gradients for use in these methods is tedious work, and formulating second order derivatives is even more laborious. Additionally, second order techniques often require the storage and inversion of large matrices of partial derivatives, with memory requirements that can be prohibitive for data-rich imaging modalities. We use a reverse-mode automatic differentiation (AD) framework to implement an efficient matrix-free version of the Levenberg-Marquardt (LM) algorithm, a longstanding method that finds popular use in nonlinear least-square minimization problems but which has seen little use in phase retrieval. Furthermore, we extend the basic LM algorithm so that it can be applied for more general constrained optimization problems (including phase retrieval problems) beyond just the least-square applications. Since we use AD, we only need to specify the physics-based forward model for a specific imaging application; the first and second-order derivative terms are calculated automatically through matrix-vector products, without explicitly forming the large Jacobian or Gauss-Newton matrices typically required for the LM method. We demonstrate that this algorithm can be used to solve both the unconstrained ptychographic object retrieval problem and the constrained “blind” ptychographic object and probe retrieval problems, under the popular Gaussian noise model as well as the Poisson noise model. We compare this algorithm to state-of-the-art first order ptychographic reconstruction methods to demonstrate empirically that this method outperforms best-in-class first-order methods: it provides excellent convergence guarantees with (in many cases) a superlinear rate of convergence, all with a computational cost comparable to, or lower than, the tested first-order algorithms.

36 MATERIALS SCIENCE↗
NASA NTRS1976

Electrostatic field changes produced by Florida lightning

The electrical behavior of thunderstorms triggered by local heating and sea-breeze convergence, a low pressure disturbance, and a weak frontal passage has been studied at the NASA Kennedy Space Center, Florida. A nonlinear least-squares minimization procedure has been developed to describe changes in the total electrostatic field produced by lightning in terms of point charge models for the cloud charge distributions. The results indicate that discharges to ground usually neutralize cloud charges in the range from -10 to -40 C. The computed charge altitudes for Florida are somewhat higher than for other geographical locations, 6 to 9.5 km, but the corresponding ambient air temperatures, -10 to -34 C, are similar. A large fraction of the discharges to ground show total field changes which are small or even reversed in polarity within 3 km of the discharges. It is suggested that ground discharges often neutralize a small positive charge, 0.5 to 4 C at altitudes of 1 to 3 km, in addition to the larger negative charge higher in the cloud.

Jacobson, E. A.↗
NASA NTRS1982

Line positions and strengths of HDO in the 2400-3300 per cm region

The vibration-rotation spectrum of HDO in the 2400-3300 per cm region has been studied at 0.01 per cm resolution with a Fourier transform spectrometer. Values of the ground state levels and levels in the (100) and (020) states have been determined from the data. The ground state levels are fitted to a Watson-type Hamiltonian from which 17 rotational constants are obtained. Measurements of the strengths of over 1100 lines have been made using a nonlinear least-squares fitting technique, and 548 of these lines are analyzed to determine the band strengths, the coefficients of the F factors, and the Coriolis interaction parameters. The strengths of the A- and B-type (100) bands and the A- and B-type (020) bands are 53.2 + or - 0.9, 0.43 + or - 0.07, 6.00 + or - 0.54, and 2.75 + or - 0.12 per sq cm per atm at 296 K, respectively.

Toth, R. A.↗
NASA NTRS1982

Stratospheric N2O mixing ratio profile from high-resolution balloon-borne solar absorption spectra and laboratory spectra near 1880/cm

A nonlinear least-squares fitting procedure is used to derive the stratospheric N2O mixing ratio profile from balloon-borne solar absorption spectra and laboratory spectra near 1880/cm. The atmospheric spectra analyzed here were recorded during sunset from a float altitude of 33 km with the University of Denver's 0.02/cm resolution interferometer near Alamogordo, N.M. (33 deg N) on Oct. 10, 1979. The laboratory data are used to determine the N2O line intensities. The measurements suggest an N2O mixing ratio of 264 ppbv near 15 km, decreasing to 155 ppbv near 28 km.

Rinsland, C. P.↗
NASA NTRS1983

Absolute intensity measurements of the (11/1/0)II-00/0/0 band of (C-12)(O-16)2 at 5.2 microns

A nonlinear least-squares fitting procedure has been used to derive absolute intensities for lines in the P, R, and Q branches of the (11/1/0)II-00/0/0 band of (C-12)(O-16)2 (band center = 1932/cm) from long-path 0.01/cm resolution laboratory spectra. The spectral data were recorded at room temperature and low pressure (less than 10 torr) with the Fourier transform spectrometer in the McMath solar telescope complex at Kitt Peak National Observatory. The observed line intensities were analyzed to derive the vibrational band intensity and F-factor coefficients. To obtain a good fit to the data, it was necessary to include terms in the expression for the F factor, which account for Coriolis-type and Fermi-type interactions and centrifugal distortion effects.

Rinsland, C. P.↗
NASA NTRS1984

Analysis and application of Fourier transform spectroscopy in atmospheric remote sensing

An analysis method for Fourier transform spectroscopy is summarized with applications to various types of distortion in atmospheric absorption spectra. This analysis method includes the fast Fourier transform method for simulating the interferometric spectrum and the nonlinear least-squares method for retrieving the information from a measured spectrum. It is shown that spectral distortions can be simulated quite well and that the correct information can be retrieved from a distorted spectrum by this analysis technique.

Park, J. H.↗
NASA NTRS1985

Calculations of microwave brightness temperature of rough soil surfaces: Bare field

A model for simulating the brightness temperatures of soils with rough surfaces is developed. The surface emissivity of the soil media is obtained by the integration of the bistatic scattering coefficients for rough surfaces. The roughness of a soil surface is characterized by two parameters, the surface height standard deviation sigma and its horizontal correlation length l. The model calculations are compared to the measured angular variations of the polarized brightness temperatures at both 1.4 GHz and 5 GHz frequences. A nonlinear least-squares fitting method is used to obtain the values of delta and l that best characterize the surface roughness. The effect of shadowing is incorporated by introducing a function S(theta), which represents the probability that a point on a rough surface is not shadowed by other parts of the surface. The model results for the horizontal polarization are in excellent agreement with the data. However, for the vertical polarization, some discrepancies exist between the calculations and data, particularly at the 1.4 GHz frequency. Possible causes of the discrepancy are discussed.

Mo, T.↗
NASA NTRS1984

Absolute intensity measurements of CO2 bands in the 2395-2680/cm region

Absolute intensities for over 800 transitions belonging to twelve bands of (C-12)(O-16)2, (O-16)(C-12)(O-18), (O-16)(C-12)(O-17), and (O-16)(C-13)(O-18) molecules in the 2395-2680/cm spectral region have been derived using a nonlinear least-squares spectral fitting procedure. The data used in the analysis were recorded at room temperature and low pressure with the 0.01/cm resolution Fourier transform spectrometer in the McMath solar telescope complex at the National Solar Observatory. The measured intensities obtained for each band have been analyzed to derive the vibrational band intensity and F-factor coefficients. The results are compared with other published values.

Malathy Devi, V.↗
NASA NTRS1984

Absolute intensities of spectral lines in carbon dioxide bands near 2050/cm

The absolute intensities of individual lines of eleven relatively weak bands of (C-12)(O-16)2, (C-13)(O-16)2, (O-16)(C-12)(O-18), and (O-16)(C-12)(O-17) near 2050/cm were measured and recorded at room temperature and 0.01/cm resolution with the Fourier transform spectrometer located in the McMath solar telescope complex located at the National Solar Observatory on Kitt Peak. Each spectrum was obtained with an integration time of one hour, the temperature and pressure were monitored during this time, and the signal-to-rms noise in the 5 micron region was approximately 4000 for all scans. The intensities were determined from analysis of 1-2/cm segments of spectra using nonlinear least-squares spectral curve fitting, and analyzed to determine the vibrational band intensity and F-factor coefficients for each of the bands. The results are pertinent to a wide variety of problems in atmospheric physics and for the analysis of remote-sensing data.

Rinsland, C. P.↗
NASA NTRS1984

Experimental determination of the 1 Sigma(+) state electric dipole moment function of carbon monoxide up to a large internuclear separation

Experimental intensity information is combined with numerically obtained vibrational wave functions in a nonlinear least-squares fitting procedure to obtain the ground electronic state electric dipole moment function of carbon monoxide valid in the range of nuclear oscillation (0.87-1.91 A) of about the V = 38th vibrational level. Vibrational transition matrix elements are computed from this function for Delta V = 1, 2, 3 with V not more than 38.

Chackerian, C., Jr.↗
NASA NTRS1983

Analysis of 12-700 micron reflectance spectra of three optical black samples

Normal incidence, specular reflectance spectra of three samples of optical black coatings have been measured in 10 filter passbands at effective wavelengths between 12 and 700 microns. Strong absorption, due to amorphous silicate material in the coatings, is found in the 15-50 micron region of each spectrum. Reflecting-layer model calculations are fitted by a nonlinear least-squares routine to the spectra at wavelengths beyond the absorption band to determine far-infrared optical parameters. It is found that, with a similar wavelength dependence, the absorption coefficient of a new black coating (ECP 2200) made by the Minnesota Mining and Manufacturing Company (3M) is less than 1/10 that of the discontinued coating, 3M Black Velvet Nextel. It is also shown that the extinction effect of a very rough substrate is negligible compared with the effects of increased upper surface roughness and coating thickness attendant upon fully covering a very rough substrate.

Smith, S. M.↗
NASA NTRS1985

Measurements of absolute line intensities in carbon dioxide bands near 5.2 microns

A nonlinear least-squares spectral fitting procedure has been used to derive experimental absolute intensities for over 300 unblended lines belonging to twelve CO2 bands in the 5.2-micron region. The spectral data were recorded at 0.01/cm resolution and room temperature with the Fourier transform spectrometer in the McMath solar telescope complex at the National Solar Observatory on Kitt Peak and have a signal-to-rms noise ratio of 2000-4000. A natural sample of carbon dioxide was used as the sample gas. For each band, the measured line intensities have been analyzed to derive the vibrational band intensity and coefficients of the F factor. The results are compared to the values used to calculate the intensities in the 1982 Air Force Geophysics Laboratory line parameters compilation.

Rinsland, C. P.↗