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Towards beating the curse of dimensionality for gravitational waves using reduced basis

Field, Scott E. and Galley, Chad R. and Ochsner, Evan (2012) Towards beating the curse of dimensionality for gravitational waves using reduced basis. Physical Review D, 86 (8). Art. No. 084046. ISSN 2470-0010.

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Using the reduced basis approach, we efficiently compress and accurately represent the space of waveforms for nonprecessing binary black hole inspirals, which constitutes a four-dimensional parameter space (two masses, two spin magnitudes). Compared to the nonspinning case, we find that only a marginal increase in the (already relatively small) number of reduced basis elements is required to represent any nonprecessing 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 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 m_1/m_2 of nonspinning binaries selected by the algorithm are mostly in the interval [1,3] and that the median of the distribution follows a power-law behavior ∼(m_1/m_2)^(-5.25).

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Additional Information:© 2012 American Physical Society. Received 29 May 2012; published 23 October 2012. This work has been supported by NSF Grants No. PHY1208861 and No. PHY1005632 to the University of Maryland, and NSF Grant No. PHY0970074 to the University of Wisconsin-Milwaukee. C. G. was supported by an appointment to the NASA Postdoctoral Program at the Jet Propulsion Laboratory administered by Oak Ridge Associated Universities through a contract with NASA. Copyright 2012. All rights reserved. We thank Alessandra Buonanno, Sarah Caudill, Tom Dent, Alexandre Le Tiec, Drew Keppel, and Dianne O’Leary for very helpful comments on the manuscript and/or suggestions.We especially thank Manuel Tiglio for helpful discussions and comments on the manuscript as well as generating much of the data used in this paper.
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NASA Postdoctoral ProgramUNSPECIFIED
Issue or Number:8
Classification Code:PACS: 04.80.Nn, 04.25.dg
Record Number:CaltechAUTHORS:20121130-095915373
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:35748
Deposited By: Tony Diaz
Deposited On:05 Dec 2012 19:45
Last Modified:03 Oct 2019 04:31

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