6,118 research outputs found
An architecture for efficient gravitational wave parameter estimation with multimodal linear surrogate models
The recent direct observation of gravitational waves has further emphasized
the desire for fast, low-cost, and accurate methods to infer the parameters of
gravitational wave sources. Due to expense in waveform generation and data
handling, the cost of evaluating the likelihood function limits the
computational performance of these calculations. Building on recently developed
surrogate models and a novel parameter estimation pipeline, we show how to
quickly generate the likelihood function as an analytic, closed-form
expression. Using a straightforward variant of a production-scale parameter
estimation code, we demonstrate our method using surrogate models of
effective-one-body and numerical relativity waveforms. Our study is the first
time these models have been used for parameter estimation and one of the first
ever parameter estimation calculations with multi-modal numerical relativity
waveforms, which include all l <= 4 modes. Our grid-free method enables rapid
parameter estimation for any waveform with a suitable reduced-order model. The
methods described in this paper may also find use in other data analysis
studies, such as vetting coincident events or the computation of the
coalescing-compact-binary detection statistic.Comment: 10 pages, 3 figures, and 1 tabl
Towards beating the curse of dimensionality for gravitational waves using Reduced Basis
Using the Reduced Basis approach, we efficiently compress and accurately
represent the space of waveforms for non-precessing binary black hole
inspirals, which constitutes a four dimensional parameter space (two masses,
two spin magnitudes). Compared to the non-spinning case, we find that only a
{\it marginal} increase in the (already relatively small) number of reduced
basis elements is required to represent any non-precessing waveform to nearly
numerical round-off precision. Most parameters selected by the algorithm are
near the boundary of the parameter space, leaving the bulk of its volume
sparse. Our results suggest that the full eight dimensional space (two masses,
two spin magnitudes, four spin orientation angles on the unit sphere) may be
highly compressible and represented with very high accuracy by a remarkably
small number of waveforms, thus providing some hope that the number of
numerical relativity simulations of binary black hole coalescences needed to
represent the entire space of configurations is not intractable. Finally, we
find that the {\it distribution} of selected parameters is robust to different
choices of seed values starting the algorithm, a property which should be
useful for indicating parameters for numerical relativity simulations of binary
black holes. In particular, we find that the mass ratios of
non-spinning binaries selected by the algorithm are mostly in the interval
and that the median of the distribution follows a power-law behavior
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
Learning orbital dynamics of binary black hole systems from gravitational wave measurements
We introduce a gravitational waveform inversion strategy that discovers
mechanical models of binary black hole (BBH) systems. We show that only a
single time series of (possibly noisy) waveform data is necessary to construct
the equations of motion for a BBH system. Starting with a class of universal
differential equations parameterized by feed-forward neural networks, our
strategy involves the construction of a space of plausible mechanical models
and a physics-informed constrained optimization within that space to minimize
the waveform error. We apply our method to various BBH systems including
extreme and comparable mass ratio systems in eccentric and non-eccentric
orbits. We show the resulting differential equations apply to time durations
longer than the training interval, and relativistic effects, such as perihelion
precession, radiation reaction, and orbital plunge, are automatically accounted
for. The methods outlined here provide a new, data-driven approach to studying
the dynamics of binary black hole systems
Persistent junk solutions in time-domain modeling of extreme mass ratio binaries
In the context of metric perturbation theory for non-spinning black holes,
extreme mass ratio binary (EMRB) systems are described by distributionally
forced master wave equations. Numerical solution of a master wave equation as
an initial boundary value problem requires initial data. However, because the
correct initial data for generic-orbit systems is unknown, specification of
trivial initial data is a common choice, despite being inconsistent and
resulting in a solution which is initially discontinuous in time. As is well
known, this choice leads to a "burst" of junk radiation which eventually
propagates off the computational domain. We observe another unintended
consequence of trivial initial data: development of a persistent spurious
solution, here referred to as the Jost junk solution, which contaminates the
physical solution for long times. This work studies the influence of both types
of junk on metric perturbations, waveforms, and self-force measurements, and it
demonstrates that smooth modified source terms mollify the Jost solution and
reduce junk radiation. Our concluding section discusses the applicability of
these observations to other numerical schemes and techniques used to solve
distributionally forced master wave equations.Comment: Uses revtex4, 16 pages, 9 figures, 3 tables. Document reformatted and
modified based on referee's report. Commentary added which addresses the
possible presence of persistent junk solutions in other approaches for
solving master wave equation
Fast and accurate prediction of numerical relativity waveforms from binary black hole coalescences using surrogate models
Simulating a binary black hole (BBH) coalescence by solving Einstein's
equations is computationally expensive, requiring days to months of
supercomputing time. Using reduced order modeling techniques, we construct an
accurate surrogate model, which is evaluated in a millisecond to a second, for
numerical relativity (NR) waveforms from non-spinning BBH coalescences with
mass ratios in and durations corresponding to about orbits
before merger. We assess the model's uncertainty and show that our modeling
strategy predicts NR waveforms {\em not} used for the surrogate's training with
errors nearly as small as the numerical error of the NR code. Our model
includes all spherical-harmonic waveform modes resolved by
the NR code up to We compare our surrogate model to Effective One
Body waveforms from - for advanced LIGO detectors and find
that the surrogate is always more faithful (by at least an order of magnitude
in most cases).Comment: Updated to published version, which includes a section comparing the
surrogate and effective-one-body models. The surrogate is publicly available
for download at http://www.black-holes.org/surrogates/ . 6 pages, 6 figure
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