20 research outputs found
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
Parameterized tests of the strong-field dynamics of general relativity using gravitational wave signals from coalescing binary black holes: Fast likelihood calculations and sensitivity of the method
Thanks to the recent discoveries of gravitational wave signals from binary
black hole mergers by Advanced Laser Interferometer Gravitational Wave
Observatory and Advanced Virgo, the genuinely strong-field dynamics of
spacetime can now be probed, allowing for stringent tests of general relativity
(GR). One set of tests consists of allowing for parametrized deformations away
from GR in the template waveform models and then constraining the size of the
deviations, as was done for the detected signals in previous work. In this
paper, we construct reduced-order quadratures so as to speed up likelihood
calculations for parameter estimation on future events. Next, we explicitly
demonstrate the robustness of the parametrized tests by showing that they will
correctly indicate consistency with GR if the theory is valid. We also check to
what extent deviations from GR can be constrained as information from an
increasing number of detections is combined. Finally, we evaluate the
sensitivity of the method to possible violations of GR.Comment: 19 pages, many figures. Matches PRD versio
On ab initio-based, free and closed-form expressions for gravitational waves
We introduce a new approach for fnding high accuracy, free and closed-form expressions for the gravitational waves emitted by binary black hole collisions from ab initio models. More precisely, our expressions are built from numerical surrogate models based on supercomputer simulations of the Einstein equations, which have been shown to be essentially indistinguishable from each other. Distinct aspects of our approach are that: (i) representations of the gravitational waves can be explicitly written in a few lines, (ii) these representations are free-form yet still fast to search for and validate and (iii) there are no underlying physical approximations in the underlying model. The key strategy is combining techniques from Artifcial Intelligence and Reduced Order Modeling for parameterized systems. Namely, symbolic regression through genetic programming combined with sparse representations in parameter space and the time domain using Reduced Basis and the Empirical Interpolation Method enabling fast free-form symbolic searches and large-scale a posteriori validations. As a proof of concept we present our results for the collision of two black holes, initially without spin, and with an initial separation corresponding to 25–31 gravitational wave cycles before merger. The minimum overlap, compared to ground truth solutions, is 99%. That is, 1% diference between our closed-form expressions and supercomputer simulations; this is considered for gravitational (GW) science more than the minimum required due to experimental numerical errors which otherwise dominate. This paper aims to contribute to the feld of GWs in particular and Artifcial Intelligence in general.Fil: Tiglio, Manuel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Villanueva, Uziel Aarón. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentin
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