Search NASA⌕ Search

SEARCH · Search NASA

Results for “variational method”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 793 records · Page 44

Simulating scalar field theories on quantum computers with limited resources

Here we present a quantum algorithm for implementing φ 4 lattice scalar field theory on qubit computers. The field is represented in the discretized field amplitude basis. The number of qubits and elementary gates required by the implementation of the evolution operator is proportional to the lattice size. The algorithm allows efficient φ 4 state preparation for a large range of input parameters in both the normal and broken-symmetry phases. The states are prepared using a combination of variational and adiabatic evolution methods. First, the ground state of a local Hamiltonian, which includes the φ 4 self-interaction, is prepared using short variational circuits. Next, this state is evolved by switching on the coupling between the lattice sites adiabatically. The parameters defining the local Hamiltonian are adjustable and constitute the input of our algorithm. We present a method to optimize these parameters in order to reduce the adiabatic time required for state preparation. For preparing broken-symmetry states, the adiabatic evolution problems caused by crossing the phase transition critical line and by the degeneracy of the broken-symmetry ground state can be addressed using an auxiliary external field which gradually turns off during the adiabatic process. We show that the time dependence of the external field during the adiabatic evolution is important for addressing the broken-symmetry ground state degeneracy. The adiabatic time dependence on the inverse error tolerance can be reduced from quadratic to linear by using a field strength that decreases exponentially in time relative to one that decreases linearly.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Synchronous and Concurrent Multidomain Computing Method for Cloud Computing Platforms

We present a numerical method for synchronous and concurrent solution of transient elastodynamics problem where the computational domain is divided into subdomains that may reside on separate computational platforms. Here, this work employs the variational multiscale discontinuous Galerkin (VMDG) method to develop interdomain transmission conditions for transient problems. The fine-scale modeling concept leads to variationally consistent coupling terms at the common interfaces. The method admits a large class of time discretization schemes, and decoupling of the solution for each subdomain is achieved by selecting any explicit algorithm. Numerical tests with a manufactured solution problem show optimal convergence rates. The energy history in a free vibration problem is in agreement with that of the solution from a monolithic computational domain.

97 MATHEMATICS AND COMPUTING↗

A New Method to Retrieve the Diurnal Variability of Planetary Boundary Layer Height from Lidar Under Different Thermodynamic Stability Conditions

The planetary boundary layer height (PBLH) is an important parameter for understanding the accumulation of pollutants and the dynamics of the lower atmosphere. Lidar has been used for tracking the evolution of PBLH by using aerosol backscatter as a tracer, assuming aerosol is generally well-mixed in the PBL; however, the validity of this assumption actually varies with atmospheric stability. This is demonstrated here for stable boundary layers (SBL), neutral boundary layers (NBL), and convective boundary layers (CBL) using an 8-year dataset of micropulse lidar (MPL) and radiosonde (RS) measurements at the ARM Southern Great Plains, and MPL at the GSFC site. Due to weak thermal convection and complex aerosol stratification, traditional gradient and wavelet methods can have difficulty capturing the diurnal PBLH variations in the morning and forenoon, as well as under stable conditions generally. A new method is developed that combines lidar-measured aerosol backscatter with a stability dependent model of PBLH temporal variation (DTDS). The latter helps “recalibrate” the PBLH in the presence of a residual aerosol layer that does not change in harmony with PBL diurnal variation. The hybrid method offers significantly improved PBLH detection, with better correlation and smaller biases, under most thermodynamic conditions, especially for SBL and CBL. Relying on the physical process of PBL diurnal development, different schemes are developed for growing, maintenance, and decaying periods. Comprehensive evaluation of this new method shows much better tracking of diurnal PBLH variation and significantly smaller biases under various pollution levels.

Tianning Su↗

Random motion analysis of flexible satellite structures

A singular perturbation formulation is used to study the responses of a flexible satellite when random measurement errors can occur. The random variables, at different instants of time, are assumed to be uncorrelated. Procedures for obtaining maxima and minima are described, and a variation of the linear method is developed for the formal solution of the two-point boundary-value problems represented by the variational equations. Random and deterministic solutions for the structural position coordinates are studied, and an analytic algorithm for treating the force equation of motion is developed. Since the random system indicated by the variational equation will always be asymptotically unstable, any analysis of stability must be based on the deterministic system.

Huang, T. C.↗

Delta Method Application for the Correlation of IR Detector Thermal Parasitic Loads with Statistically Accurate Results

The Linear Etalon Imaging Spectral Array (LEISA) is a cryogenic IR detector that is passively cooled below 110K. LEISA is part of the L’Ralph instrument, which is going on the Lucy mission, with planned flyby’s of the Trojan asteroids around 5.5 AU. One of the primary thermal challenges is to successfully quantify each significant parasitic heat flow value with statistical certainty.Simulation of flight-like thermal environments and correlation of thermal models is an important part of this challenge, which can be critical for thermally sensitive systems such as cryogenic detectors that are passively cooled. It is common practice during TVAC to achieve several thermal balance points and then to correlate several design variables in order to achieve the closest match to all balance points tested. This approach lends itself to high levels of uncertainty in the correlated values due to the cumulative effect of absolute temperature uncertainty and differences between the sensors used for the measurement. Accuracy can be improved with the use of more accurate sensors, by calibrating all sensors with respect to each other, and by using Zero-Q methodologies, all of which add cost and complexity to the test.The Delta Method uses the difference in temperature caused by the changes in the boundary conditions to calculate heat flows and/or thermal resistances across temperature differentials. This eliminates the problem of high uncertainties with absolute temperature measurements, and yields statistically accurate results down to the sensor resolution of 1mK at < 100K, by taking the sensor’s calibration errors out of the equation. During testing, this method relies on parametric variations around an initial balance point, by varying the boundary conditions of the different parasitic heat sources. The Delta Method, as well as its application on the LEISA thermal test, will be discussed in detail.

Daniel G. Bae↗

Deeply uncertain: comparing methods of uncertainty quantification in deep learning algorithms

We present a comparison of methods for uncertainty quantification (UQ) in deep learning algorithms in the context of a simple physical system. Three of the most common uncertainty quantification methods - Bayesian Neural Networks (BNN), Concrete Dropout (CD), and Deep Ensembles (DE) - are compared to the standard analytic error propagation. We discuss this comparison in terms endemic to both machine learning ("epistemic" and "aleatoric") and the physical sciences ("statistical" and "systematic"). The comparisons are presented in terms of simulated experimental measurements of a single pendulum - a prototypical physical system for studying measurement and analysis techniques. Our results highlight some pitfalls that may occur when using these UQ methods. For example, when the variation of noise in the training set is small, all methods predicted the same relative uncertainty independently of the inputs. This issue is particularly hard to avoid in BNN. On the other hand, when the test set contains samples far from the training distribution, we found that no methods sufficiently increased the uncertainties associated to their predictions. This problem was particularly clear for CD. In light of these results, we make some recommendations for usage and interpretation of UQ methods.

59 BASIC BIOLOGICAL SCIENCES↗

On the Measurement of Elemental Abundance Ratios in Inner Galaxy H II Regions

Although abundance gradients in the Milky Way Galaxy certainly exist, details remain uncertain, particularly in the inner Galaxy, where stars and H II regions in the Galactic plane are obscured optically. In this paper we revisit two previously studied, inner Galaxy H II regions: G333.6-0.2 and W43. We observed three new positions in G333.6-0.2 with the Kuiper Airborne Observatory and reobserved the central position with the Infrared Space Observatory's Long Wavelength Spectrometer in far-infrared lines of S++, N++, N+, and O++. We also added the N+ lines at 122 and 205 microns to the suite of lines measured in W43 by Simpson et al.. The measured electron densities range from approx. 40 to over 4000 per cu cm in a single HII region, indicating that abundance analyses must consider density variations, since the critical densities of the observed lines range from 40 to 9000 per cu cm. We propose a method to handle density variations and make new estimates of the S/H and N/H abundance ratios. We find that our sulfur abundance estimates for G333.6-0.2 and W43 agree with the S/H abundance ratios expected for the gradient previously reported by Simpson et al., with the S/H values revised to be smaller owing to changes in collisional excitation cross sections. The estimated N/H, S/H, and N/S ratios are the most reliable because of their small corrections for unseen ionization states (< or approx. 10%). The estimated N/S ratios for the two sources are smaller than what would be calculated from the N/H and S/H ratios in our previous paper. If all low excitation H II regions had similar changes to their N/S ratios as a result of adding measurements of N+ to previous measurements of N++, there would be no or only a very small gradient in N/S. This is interesting because nitrogen is considered to be a secondary element and sulfur is a primary element in galactic chemical evolution calculations. We compute models of the two H II regions to estimate corrections for the other unseen ionization states. We find, with large uncertainties, that oxygen does not, have a high abundance, with the result that the N/O ratio is as high (approx. 0.35) as previously reported. The reasons for the uncertainty in the ionization corrections for oxygen are both the non-uniqueness of the H II region models and the sensitivity of these models to different input atomic data and stellar atmosphere models. We discuss these predictions and conclude that only a few of the latest models adequately reproduce H II region observations, including the well-known, relatively-large observed Ne++/O++ ratios in low- and moderate-excitation H II regions.

Simpson, Janet P.↗

Extending A Correction Method for Unsteady Transonic Aerodynamics to Variable Camber Continuous Trailing Edge Flap

In this study, we have extended our correction method for transonic aerodynamics to baseline and variable camber continuous trailing edge (VCCTEF) geometries of super-critical airfoils at cruise conditions. This correction method modifies Theodorsen theory, which is based on incompressible potential flow over a flat plate. The method is partly based on CFD RANS simulations of oscillating NASA generic transport model (GTM) baseline cruise and VCCTEF airfoil geometries in pitch and shows promise for addressing transonic flutter problems of aeroelasticity. In the earlier study1, the Theodorsen functions were modulated with non-linear functions of Mach number, M, and reduced frequency, k, and thus the correction was demonstrated for the symmetrical NACA0012 airfoil. In the present study, the modulation functions are also allowed to account for the effects of camber and thickness of the airfoil. This is demonstrated by applying the correction method to various symmetric NACA00xx airfoil geometries (NACA001, NACA0002, NACA0012, NACA0015 and NACA0018), the NASA GTM super-critical baseline and VCCTEF airfoil geometries, e.g., the circular airfoil, VCCTEF222. First results indicate that the correction method accounts for a large variation of thickness of airfoils and camber. The present correction method will guide the development of a new state space model for the VCCTEF system and eventually a new transfer function that will be incorporated in a new aeroelastic framework leading to an appropriate transonic flutter model for use in the future aircraft systems in development under the NASA Advanced Air Transportation Technologies (AATT) project.

Kaul, Upender K.↗

Analysis of Long-Term Quality Control Data for a 137 Cs Dosimetry Calibration Source

Strict quality assurance programs are required for many radiological applications, but these seldom exist for verifying dosimetry calibration sources. After initial characterization of a dosimetry calibration facility, quality control procedures are recommended to ensure the early detection of any changes or malfunctions. These also result in refined knowledge about average dose rate and experimental variations in dose delivery. This paper describes the implementation of a phase I quality control protocol for a 137 Cs dosimetry calibration source and includes an analysis of the resulting data collected over a 24-mo period. During this time, substantial data was collected to establish trial control limits. Air kerma rate measurements were obtained using an ion chamber and were adjusted for decay, corrected for ambient temperature, pressure and humidity, and then analyzed using quality control charts. Three variations of rational subgrouping methods were used in order to find assignable causes of error, and Nelson's Rules were followed to detect any non-random statistical variations. Measurements were subgrouped according to same-day measurements in order to detect positional errors as well as atmospheric correction errors. Additionally, measurements were subgrouped according to analogous experimental setups in order to detect failure in equipment or incorrect settings. Both were analyzed using the X-bar and R chart method. Similarly, individuals and moving ranges charts were used to carefully examine each position in order to observe any situational errors that may occur which include timing, positional, or interference errors. Each method was successful in identifying unique out-of-control data points that occurred during the phase I application of forming control limits. Furthermore, over the 24-mo period, enough data points were deemed in-control to establish reliable trial limits. Future experiments will include the phase II application of gaining more reliable measurements in order to fine-tune the limits, as well as performing a designed experiment, where variables are purposefully changed in order to test the variation of the data.

61 RADIATION PROTECTION AND DOSIMETRY↗

A new method to retrieve the diurnal variability of planetary boundary layer height from lidar under different thermodynamic stability conditions

The planetary boundary layer height (PBLH) is an important parameter for understanding the accumulation of pollutants and the dynamics of the lower atmosphere. Lidar has been used for tracking the evolution of PBLH by using aerosol backscatter as a tracer, assuming aerosol is generally well-mixed in the PBL; however, the validity of this assumption actually varies with atmospheric stability. This is demonstrated here for stable boundary layers (SBL), neutral boundary layers (NBL), and convective boundary layers (CBL) using an 8-year dataset of micropulse lidar (MPL) and radiosonde (RS) measurements at the ARM Southern Great Plains, and MPL at the GSFC site. Due to weak thermal convection and complex aerosol stratification, traditional gradient and wavelet methods can have difficulty capturing the diurnal PBLH variations in the morning and forenoon, as well as under stable conditions generally. Here a new method is developed that combines lidar-measured aerosol backscatter with a stability dependent model of PBLH temporal variation (DTDS). The latter helps “recalibrate” the PBLH in the presence of a residual aerosol layer that does not change in harmony with PBL diurnal variation. The hybrid method offers significantly improved PBLH detection, with better correlation and smaller biases, under most thermodynamic conditions, especially for SBL and CBL. Relying on the physical process of PBL diurnal development, different schemes are developed for growing, maintenance, and decaying periods. Comprehensive evaluation of this new method shows much better tracking of diurnal PBLH variation and significantly smaller biases under various pollution levels.

54 ENVIRONMENTAL SCIENCES↗

A method for calculating laminar viscous, compressible flows with small pressure gradients

A method is presented for calculating laminar viscous, compressible flows in which pressure gradients are assumed to be neglibible in energy conservation and in developing property relations, but not in momentum conservation. The equations are developed from Navier-Stokes equations in a noninertial reference frame. The method is an extension of an approximate method developed for calculating combined forced and contained natural convection in a rotating tank. The restriction to small density and temperature variations in the previous method is removed. For illustration, a two-dimensional simulation of the rotating tank problem is formulated, and the numerical computation procedure to be used is indicated.

Martin, E. D.↗

Implications of the Observed Mesoscale Variations of Clouds for Earth's Radiation Budget

The effect of small-spatial-scale cloud variations on radiative transfer in cloudy atmospheres currently receives a lot of research attention, but the available studies are not very clear about which spatial scales are important and report a very large range of estimates of the magnitude of the effects. Also, there have been no systematic investigations of how to measure and represent these cloud variations. We exploit the cloud climatology produced by the International Satellite Cloud Climatology Project (ISCCP) to: (1) define and test different methods of representing cloud variation statistics, (2) investigate the range of spatial scales that should be included, (3) characterize cloud variations over a range of space and time scales covering mesoscale (30 - 300 km, 3-12 hr) into part of the lower part of the synoptic scale (300 - 3000 km, 1-30 days), (4) obtain a climatology of the optical thickness, emissivity and cloud top temperature variability of clouds that can be used in weather and climate GCMS, together with the parameterization proposed by Cairns et al. (1999), to account for the effects of small-scale cloud variations on radiative fluxes, and (5) evaluate the effect of observed cloud variations on Earth's radiation budget. These results lead to the formulation of a revised conceptual model of clouds for use in radiative transfer calculations in GCMS. The complete variability climatology can be obtained from the ISCCP Web site at http://isccp.giss.nasa.gov.

Rossow, William B.↗

Use of the single-breath method of estimating cardiac output during exercise-stress testing.

The single-breath cardiac output measurement technique of Kim et al. (1966) has been modified for use in obtaining cardiac output measurements during exercise-stress tests on Apollo astronauts. The modifications involve the use of a respiratory mass spectrometer for data acquisition and a digital computer program for data analysis. The variation of the modified method for triplicate steady-state cardiac output measurements was plus or minus 1 liter/min. The combined physiological and methodological variation seen during a set of three exercise tests on a series of subjects was 1 to 2.5 liter/min. Comparison of the modified method with the direct Fick technique showed that although the single-breath values were consistently low, the scatter of data was small and the correlation between the two methods was high. Possible reasons for the low single-breath cardiac output values are discussed.

Buderer, M. C.↗

Non‐Linear Dimensionality Reduction With a Variational Encoder Decoder to Understand Convective Processes in Climate Models

Abstract Deep learning can accurately represent sub‐grid‐scale convective processes in climate models, learning from high resolution simulations. However, deep learning methods usually lack interpretability due to large internal dimensionality, resulting in reduced trustworthiness in these methods. Here, we use Variational Encoder Decoder structures (VED), a non‐linear dimensionality reduction technique, to learn and understand convective processes in an aquaplanet superparameterized climate model simulation, where deep convective processes are simulated explicitly. We show that similar to previous deep learning studies based on feed‐forward neural nets, the VED is capable of learning and accurately reproducing convective processes. In contrast to past work, we show this can be achieved by compressing the original information into only five latent nodes. As a result, the VED can be used to understand convective processes and delineate modes of convection through the exploration of its latent dimensions. A close investigation of the latent space enables the identification of different convective regimes: (a) stable conditions are clearly distinguished from deep convection with low outgoing longwave radiation and strong precipitation; (b) high optically thin cirrus‐like clouds are separated from low optically thick cumulus clouds; and (c) shallow convective processes are associated with large‐scale moisture content and surface diabatic heating. Our results demonstrate that VEDs can accurately represent convective processes in climate models, while enabling interpretability and better understanding of sub‐grid‐scale physical processes, paving the way to increasingly interpretable machine learning parameterizations with promising generative properties.

54 ENVIRONMENTAL SCIENCES↗

Factors That Influence Variability in Stress-Drop Measurements Using Spectral Decomposition and Spectral-Ratio Methods for the 2019 Ridgecrest Earthquake Sequence

Stress drop is a fundamental parameter related to earthquake source physics, but is hard to measure accurately. To better understand how different factors influence stress-drop measurements, we compare two different methods using the Ridgecrest stress-drop validation data set: spectral decomposition (SD) and spectral ratio (SR), each with different processing options. Here, we also examine the influence of spectral complexity on source parameter measurement. Applying the SD method, we find that frequency bandwidth and time-window length could influence spectral magnitude calibration, while depth-dependent attenuation is important to correctly map stress-drop variations. For the SR method, we find that the selected source model has limited influence on the measurements; however, the Boatwright model tends to produce smaller standard deviation and larger magnitude dependence than the Brune model. Variance reduction threshold, frequency bandwidth, and time-window length, if chosen within an appropriate parameter range, have limited influence on source parameter measurement. For both methods, wave type, attenuation correction, and spectral complexity strongly influence the result. The scale factor that quantifies the magnitude dependence of stress drop show large variations with different processing options, and earthquakes with complex source spectra deviating from the Brune-type source models tend to have larger scale factor than earthquakes without complexity. Based on these detailed comparisons, we make a few specific suggestions for data processing workflows that could help future studies of source parameters and interpretations.

58 GEOSCIENCES↗

Variational inference of effective range parameters for 3 He− 4 He scattering

We use two different methods, Monte Carlo sampling and variational inference (VI), to perform a Bayesian calibration of the effective-range parameters in 3 He– 4 He elastic scattering. The parameters are calibrated to data from a recent set of 3 He– 4 He elastic scattering differential cross section measurements. Analysis of these data for E lab ≤ 4.3 MeV yields a unimodal posterior for which both methods obtain the same structure. However, the effective-range expansion amplitude does not account for the 7/2 − state of 7 Be so, even after calibration, the description of data at the upper end of this energy range is poor. The data up to E lab = 2.6 MeV can be well described, but calibration to this lower-energy subset of the data yields a bimodal posterior. After adapting VI to treat such a multi-modal posterior we find good agreement between the VI results and those obtained with parallel-tempered Monte Carlo sampling.

effective field theory↗