3,843 research outputs found
General CMB and Primordial Bispectrum Estimation I: Mode Expansion, Map-Making and Measures of f_NL
We present a detailed implementation of two bispectrum estimation methods
which can be applied to general non-separable primordial and CMB bispectra. The
method exploits bispectrum mode decompositions on the domain of allowed
wavenumber or multipole values. Concrete mode examples constructed from
symmetrised tetrahedral polynomials are given, demonstrating rapid convergence
for known bispectra. We use these modes to generate simulated CMB maps of high
resolution (l > 2000) given an arbitrary primordial power spectrum and
bispectrum or an arbitrary late-time CMB angular power spectrum and bispectrum.
By extracting coefficients for the same separable basis functions from an
observational map, we are able to present an efficient and general f_NL
estimator for a given theoretical model. The estimator has two versions
comparing theoretical and observed coefficients at either primordial or late
times, thus encompassing a wider range of models, including secondary
anisotropies, lensing and cosmic strings. We provide examples and validation of
both f_NL estimation methods by direct comparison with simulations in a
WMAP-realistic context. In addition, we show how the full bispectrum can be
extracted from observational maps using these mode expansions, irrespective of
the theoretical model under study. We also propose a universal definition of
the bispectrum parameter F_NL for more consistent comparison between
theoretical models. We obtain WMAP5 estimates of f_NL for the equilateral model
from both our primordial and late-time estimators which are consistent with
each other, as well as with results already published in the literature. These
general bispectrum estimation methods should prove useful for the analysis of
nonGaussianity in the Planck satellite data, as well as in other contexts.Comment: 41 pages, 17 figure
Fast prediction and evaluation of gravitational waveforms using surrogate models
[Abridged] We propose a solution to the problem of quickly and accurately
predicting gravitational waveforms within any given physical model. The method
is relevant for both real-time applications and in more traditional scenarios
where the generation of waveforms using standard methods can be prohibitively
expensive. Our approach is based on three offline steps resulting in an
accurate reduced-order model that can be used as a surrogate for the
true/fiducial waveform family. First, a set of m parameter values is determined
using a greedy algorithm from which a reduced basis representation is
constructed. Second, these m parameters induce the selection of m time values
for interpolating a waveform time series using an empirical interpolant. Third,
a fit in the parameter dimension is performed for the waveform's value at each
of these m times. The cost of predicting L waveform time samples for a generic
parameter choice is of order m L + m c_f online operations where c_f denotes
the fitting function operation count and, typically, m << L. We generate
accurate surrogate models for Effective One Body (EOB) waveforms of
non-spinning binary black hole coalescences with durations as long as 10^5 M,
mass ratios from 1 to 10, and for multiple harmonic modes. We find that these
surrogates are three orders of magnitude faster to evaluate as compared to the
cost of generating EOB waveforms in standard ways. Surrogate model building for
other waveform models follow the same steps and have the same low online
scaling cost. For expensive numerical simulations of binary black hole
coalescences we thus anticipate large speedups in generating new waveforms with
a surrogate. As waveform generation is one of the dominant costs in parameter
estimation algorithms and parameter space exploration, surrogate models offer a
new and practical way to dramatically accelerate such studies without impacting
accuracy.Comment: 20 pages, 17 figures, uses revtex 4.1. Version 2 includes new
numerical experiments for longer waveform durations, larger regions of
parameter space and multi-mode model
Data Driven Surrogate Based Optimization in the Problem Solving Environment WBCSim
Large scale, multidisciplinary, engineering designs are always difficult due to the complexity and dimensionality of these problems. Direct coupling between the analysis codes and the optimization routines can be prohibitively time consuming due to the complexity of the underlying simulation codes. One way of tackling this problem is by constructing computationally cheap(er) approximations of the expensive simulations, that mimic the behavior of the simulation model as closely as possible. This paper presents a data driven, surrogate based optimization algorithm that uses a trust region based sequential approximate optimization (SAO) framework and a statistical sampling approach based on design of experiment (DOE) arrays. The algorithm is implemented using techniques from two packages—SURFPACK and SHEPPACK that provide a collection of approximation algorithms to build the surrogates and three different DOE techniques—full factorial (FF), Latin hypercube sampling (LHS), and central composite design (CCD)—are used to train the surrogates. The results are compared with the optimization results obtained by directly coupling an optimizer with the simulation code. The biggest concern in using the SAO framework based on statistical sampling is the generation of the required database. As the number of design variables grows, the computational cost of generating the required database grows rapidly. A data driven approach is proposed to tackle this situation, where the trick is to run the expensive simulation if and only if a nearby data point does not exist in the cumulatively growing database. Over time the database matures and is enriched as more and more optimizations are performed. Results show that the proposed methodology dramatically reduces the total number of calls to the expensive simulation runs during the optimization process
Modal vector fitting : a tool for generating rational models of high accuracy with arbitrary terminal conditions
This paper introduces a new approach for rational macromodeling of multiport devices that ensures high accuracy with arbitrary terminal conditions. This is achieved by reformulating the vector fitting (VF) technique to focus on eigenpairs rather than matrix elements. By choosing the least squares (LS) weighting equal to the inverse of the eigenvalue magnitude, the modal components are fitted with a relative accuracy criterion. The resulting modal vector fitting (MVF) method is shown to give a major improvement in accuracy for cases with a high ratio between the largest and smallest eigenvalue, although it is computationally more costly than VF. It is also shown how to utilize the impedance characteristics of the adjacent network in the fitting process. The application of MVF is demonstrated for a two-conductor stripline, a coaxial cable, and a transformer measurement. We also show a simplified procedure which achieves similar results as MVF if the admittance matrix can be diagonalized by a constant transformation matrix. The extracted model is finally subjected to passivity enforcement by the modal perturbation method, which makes use of a similar LS formulation as MVF for the constrained optimization problem
Efficient Global Aerodynamic Modeling from Flight Data
A method for identifying global aerodynamic models from flight data in an efficient manner is explained and demonstrated. A novel experiment design technique was used to obtain dynamic flight data over a range of flight conditions with a single flight maneuver. Multivariate polynomials and polynomial splines were used with orthogonalization techniques and statistical modeling metrics to synthesize global nonlinear aerodynamic models directly and completely from flight data alone. Simulation data and flight data from a subscale twin-engine jet transport aircraft were used to demonstrate the techniques. Results showed that global multivariate nonlinear aerodynamic dependencies could be accurately identified using flight data from a single maneuver. Flight-derived global aerodynamic model structures, model parameter estimates, and associated uncertainties were provided for all six nondimensional force and moment coefficients for the test aircraft. These models were combined with a propulsion model identified from engine ground test data to produce a high-fidelity nonlinear flight simulation very efficiently. Prediction testing using a multi-axis maneuver showed that the identified global model accurately predicted aircraft responses
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