91,444 research outputs found
The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
The Gauss--Newton with approximated tensors (GNAT) method is a nonlinear
model reduction method that operates on fully discretized computational models.
It achieves dimension reduction by a Petrov--Galerkin projection associated
with residual minimization; it delivers computational efficency by a
hyper-reduction procedure based on the `gappy POD' technique. Originally
presented in Ref. [1], where it was applied to implicit nonlinear
structural-dynamics models, this method is further developed here and applied
to the solution of a benchmark turbulent viscous flow problem. To begin, this
paper develops global state-space error bounds that justify the method's design
and highlight its advantages in terms of minimizing components of these error
bounds. Next, the paper introduces a `sample mesh' concept that enables a
distributed, computationally efficient implementation of the GNAT method in
finite-volume-based computational-fluid-dynamics (CFD) codes. The suitability
of GNAT for parameterized problems is highlighted with the solution of an
academic problem featuring moving discontinuities. Finally, the capability of
this method to reduce by orders of magnitude the core-hours required for
large-scale CFD computations, while preserving accuracy, is demonstrated with
the simulation of turbulent flow over the Ahmed body. For an instance of this
benchmark problem with over 17 million degrees of freedom, GNAT outperforms
several other nonlinear model-reduction methods, reduces the required
computational resources by more than two orders of magnitude, and delivers a
solution that differs by less than 1% from its high-dimensional counterpart
An experimental study of nonlinear dynamic system identification
A technique for robust identification of nonlinear dynamic systems is developed and illustrated using both simulations and analog experiments. The technique is based on the Minimum Model Error optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature of the current work is the ability to identify nonlinear dynamic systems without prior assumptions regarding the form of the nonlinearities, in constrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length
Least-squares inversion for density-matrix reconstruction
We propose a method for reconstruction of the density matrix from measurable
time-dependent (probability) distributions of physical quantities. The
applicability of the method based on least-squares inversion is - compared with
other methods - very universal. It can be used to reconstruct quantum states of
various systems, such as harmonic and and anharmonic oscillators including
molecular vibrations in vibronic transitions and damped motion. It also enables
one to take into account various specific features of experiments, such as
limited sets of data and data smearing owing to limited resolution. To
illustrate the method, we consider a Morse oscillator and give a comparison
with other state-reconstruction methods suggested recently.Comment: 16 pages, REVTeX, 6 PS figures include
Estimation of secondary soil properties by fusion of laboratory and on-line measured vis-NIR spectra
Visible and near infrared (vis-NIR) diffuse reflectance spectroscopy has made invaluable contributions to the accurate estimation of soil properties having direct and indirect spectral responses in NIR spectroscopy with measurements made in laboratory, in situ or using on-line (while the sensor is moving) platforms. Measurement accuracies vary with measurement type, for example, accuracy is higher for laboratory than on-line modes. On-line measurement accuracy deteriorates further for secondary (having indirect spectral response) soil properties. Therefore, the aim of this study is to improve on-line measurement accuracy of secondary properties by fusion of laboratory and on-line scanned spectra. Six arable fields were scanned using an on-line sensing platform coupled with a vis-NIR spectrophotometer (CompactSpec by Tec5 Technology for spectroscopy, Germany), with a spectral range of 305-1700 nm. A total of 138 soil samples were collected and used to develop five calibration models: (i) standard, using 100 laboratory scanned samples; (ii) hybrid-1, using 75 laboratory and 25 on-line samples; (iii) hybrid-2, using 50 laboratory and 50 on-line samples; (iv) hybrid-3, using 25 laboratory and 75 on-line samples, and (v) real-time using 100 on-line samples. Partial least squares regression (PLSR) models were developed for soil pH, available potassium (K), magnesium (Mg), calcium (Ca), and sodium (Na) and quality of models were validated using an independent prediction dataset (38 samples). Validation results showed that the standard models with laboratory scanned spectra provided poor to moderate accuracy for on-line prediction, and the hybrid-3 and real-time models provided the best prediction results, although hybrid-2 model with 50% on-line spectra provided equally good results for all properties except for pH and Na. These results suggest that either the real-time model with exclusively on-line spectra or the hybrid model with fusion up to 50% (except for pH and Na) and 75% on-line scanned spectra allows significant improvement of on-line prediction accuracy for secondary soil properties using vis-NIR spectroscopy
On the Reliability of Cross Correlation Function Lag Determinations in Active Galactic Nuclei
Many AGN exhibit a highly variable luminosity. Some AGN also show a
pronounced time delay between variations seen in their optical continuum and in
their emission lines. In effect, the emission lines are light echoes of the
continuum. This light travel-time delay provides a characteristic radius of the
region producing the emission lines. The cross correlation function (CCF) is
the standard tool used to measure the time lag between the continuum and line
variations. For the few well-sampled AGN, the lag ranges from 1-100 days,
depending upon which line is used and the luminosity of the AGN. In the best
sampled AGN, NGC 5548, the H_beta lag shows year-to-year changes, ranging from
about 8.7 days to about 22.9 days over a span of 8 years. In this paper it is
demonstrated that, in the context of AGN variability studies, the lag estimate
using the CCF is biased too low and subject to a large variance. Thus the
year-to-year changes of the measured lag in NGC 5548 do not necessarily imply
changes in the AGN structure. The bias and large variance are consequences of
finite duration sampling and the dominance of long timescale trends in the
light curves, not due to noise or irregular sampling. Lag estimates can be
substantially improved by removing low frequency power from the light curves
prior to computing the CCF.Comment: To appear in the PASP, vol 111, 1999 Nov; 37 pages; 10 figure
Visual Dynamics: Probabilistic Future Frame Synthesis via Cross Convolutional Networks
We study the problem of synthesizing a number of likely future frames from a
single input image. In contrast to traditional methods, which have tackled this
problem in a deterministic or non-parametric way, we propose a novel approach
that models future frames in a probabilistic manner. Our probabilistic model
makes it possible for us to sample and synthesize many possible future frames
from a single input image. Future frame synthesis is challenging, as it
involves low- and high-level image and motion understanding. We propose a novel
network structure, namely a Cross Convolutional Network to aid in synthesizing
future frames; this network structure encodes image and motion information as
feature maps and convolutional kernels, respectively. In experiments, our model
performs well on synthetic data, such as 2D shapes and animated game sprites,
as well as on real-wold videos. We also show that our model can be applied to
tasks such as visual analogy-making, and present an analysis of the learned
network representations.Comment: The first two authors contributed equally to this wor
Toward High-Precision Astrometry with WFPC2. I. Deriving an Accurate PSF
The first step toward doing high-precision astrometry is the measurement of
individual stars in individual images, a step that is fraught with dangers when
the images are undersampled. The key to avoiding systematic positional error in
undersampled images is to determine an extremely accurate point-spread function
(PSF). We apply the concept of the {\it effective} PSF, and show that in images
that consist of pixels it is the ePSF, rather than the often-used instrumental
PSF, that embodies the information from which accurate star positions and
magnitudes can be derived. We show how, in a rich star field, one can use the
information from dithered exposures to derive an extremely accurate effective
PSF by iterating between the PSF itself and the star positions that we measure
with it. We also give a simple but effective procedure for representing spatial
variations of the HST PSF. With such attention to the PSF, we find that we are
able to measure the position of a single reasonably bright star in a single
image with a precision of 0.02 pixel (2 mas in WF frames, 1 mas in PC), but
with a systematic accuracy better than 0.002 pixel (0.2 mas in WF, 0.1 mas in
PC), so that multiple observations can reliably be combined to improve the
accuracy by .Comment: 33 pp. text + 15 figs.; accepted by PAS
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