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In a previous work, we introduced, in the context of gravitational wave science, an initial study on an automated domain-decomposition approach for a reduced basis through hp-greedy refinement. The approach constructs local reduced bases of lower dimensionality than global ones, with the same or higher accuracy. These "light" local bases should imply both faster evaluations when predicting new waveforms and faster data analysis, particularly faster statistical inference (the forward and inverse problems, respectively). In this approach, however, we have previously found important dependence on several hyperparameters, which do not appear in a global reduced basis. This naturally leads to the problem of hyperparameter optimization (HPO), which is the subject of this paper. Here, we compare the efficiency of the Bayesian approach against grid and random searches, which are two order of magnitude slower. Then, we tackle the problem of HPO through Bayesian optimization.We find that, for the cases studied here of gravitational waves from the collision of two spinning but non-precessing black holes, for the same accuracy, local hp-greedy reduced bases with HPO have a lower dimensionality of up to 4×, depending on the desired accuracy. This factor should directly translate into a parameter estimation speedup in the context of reduced order quadratures, for instance. Such acceleration might help in the near real-time requirements for electromagnetic counterparts of gravitational waves from compact binary coalescences. The code developed for this project is available open source from public repositories. This paper is an invited contribution to the Special Issue "Recent Advances in Gravity: A Themed Issue in Honor of Prof. Jorge Pullin on his 60th Anniversary". [ABSTRACT FROM AUTHOR]

We analyze a prospect for predicting gravitational waveforms from compact binaries based on automated machine learning (AutoML) from around a hundred different possible regression models, without having to resort to tedious and manual case-by-case analyses and fine-tuning. The particular study of this article is within the context of the gravitational waves emitted by the collision of two spinless black holes in initial quasi-circular orbit. We find, for example, that approaches such as Gaussian process regression with radial bases as kernels, an approach which is generalizable to multiple dimensions with low computational evaluation cost, do provide a sufficiently accurate solution. The results here presented suggest that AutoML might provide a framework for regression in the field of surrogates for gravitational waveforms. Our study is within the context of surrogates of numerical relativity simulations based on reduced basis and the empirical interpolation method, where we find that for the particular case analyzed AutoML can produce surrogates which are essentially indistinguishable from the NR simulations themselves. [ABSTRACT FROM AUTHOR]

The combination of the reduced basis and the empirical interpolation method (EIM) approaches have produced outstanding results in many disciplines. In particular, in gravitational wave (GW) science these results range from building non-intrusive surrogate models for GWs to fast parameter estimation adding the use of reduced order quadratures. These surrogates have the salient feature of being essentially indistinguishable from or very close to supercomputer simulations of the Einstein equations, but can be evaluated in the order of a millisecond per multipole mode on a standard laptop. In this article we clarify a common misperception of the EIM as originally introduced and used in practice in GW science. Namely, we prove that the EIM at each iteration chooses the interpolation nodes so as to make the related Vandermonde-type matrix as invertible as possible; not necessarily optimizing its conditioning or accuracy of the interpolant as is sometimes thought. In fact, we introduce two new variations of the EIM, nested as well, which do optimize with respect to conditioning and the Lebesgue constant, respectively, and compare them through numerical experiments with the original EIM using GWs. Our analyses and numerical results suggest a subtle relationship between solving for the original EIM, conditioning, and the Lebesgue constant, in consonance with active research in rigorous approximation theory and related fields. [ABSTRACT FROM AUTHOR]

On September 14, 2015, the newly upgraded Laser Interferometer Gravitational-wave Observatory (LIGO) recorded a loud gravitational-wave (GW) signal, emitted a billion light-years away by a coalescing binary of two stellar-mass black holes. The detection was announced in February 2016, in time for the hundredth anniversary of Einstein's prediction of GWs within the theory of general relativity (GR). The signal represents the first direct detection of GWs, the first observation of a black-hole binary, and the first test of GR in its strong-field, high-velocity, nonlinear regime. In the remainder of its first observing run, LIGO observed two more signals from black-hole binaries, one moderately loud, another at the boundary of statistical significance. The detections mark the end of a decades-long quest and the beginning of GW astronomy: finally, we are able to probe the unseen, electromagnetically dark Universe by listening to it. In this article, we present a short historical overview of GW science: this young discipline combines GR, arguably the crowning achievement of classical physics, with record-setting, ultra-low-noise laser interferometry, and with some of the most powerful developments in the theory of differential geometry, partial differential equations, high-performance computation, numerical analysis, signal processing, statistical inference, and data science. Our emphasis is on the synergy between these disciplines and how mathematics, broadly understood, has historically played, and continues to play, a crucial role in the development of GW science. We focus on black holes, which are very pure mathematical solutions of Einstein's gravitationalfield equations that are nevertheless realized in Nature and that provided the first observed signals. [ABSTRACT FROM AUTHOR]

Outer boundary conditions for strongly and symmetric hyperbolic formulations of 3D Einstein's field equations with a live gauge condition are discussed. The boundary conditions have the property that they ensure constraint propagation and control in a sense made precise in this article the physical degrees of freedom at the boundary. We use Fourier–Laplace transformation techniques to find necessary conditions for the well posedness of the resulting initial-boundary value problem and integrate the resulting three-dimensional nonlinear equations using a finite-differencing code. We obtain a set of constraint-preserving boundary conditions which pass a robust numerical stability test. We explicitly compare these new boundary conditions to standard, maximally dissipative ones through Brill wave evolutions. Our numerical results explicitly show that in the latter case the constraint variables, describing the violation of the constraints, do not converge to zero when resolution is increased while for the new boundary conditions, the constraint variables do decrease as resolution is increased. As an application, we inject pulses of "gravitational radiation" through the boundaries of an initially flat spacetime domain, with enough amplitude to generate strong fields and induce large curvature scalars, showing that our boundary conditions are robust enough to handle nonlinear dynamics. We expect our boundary conditions to be useful for improving the accuracy and stability of current binary black hole and binary neutron star simulations, for a successful implementation of characteristic or perturbative matching techniques, and other applications. We also discuss limitations of our approach and possible future directions. [ABSTRACT FROM AUTHOR]

Simulating a binary black hole 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 nonspinning binary black hole coalescences with mass ratios in [1, 10] and durations corresponding to about 15 orbits before merger. We assess the model's uncertainty and show that our modeling strategy predicts NR waveforms 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 -2Ylm waveform modes resolved by the NR code up to l = 8. We compare our surrogate model to effective one body waveforms from 50M☉ to 300M☉ for advanced LIGO detectors and find that the surrogate is always more faithful (by at least an order of magnitude in most cases). [ABSTRACT FROM AUTHOR]

Inferring the astrophysical parameters of coalescing compact binaries is a key science goal of the upcoming advanced LIGO-Virgo gravitational-wave detector network and, more generally, gravitational-wave astronomy. However, current approaches to parameter estimation for these detectors require computationally expensive algorithms. Therefore, there is a pressing need for new, fast, and accurate Bayesian inference techniques. In this Letter, we demonstrate that a reduced order modeling approach enables rapid parameter estimation to be performed. By implementing a reduced order quadrature scheme within the LIGO Algorithm Library, we show that Bayesian inference on the 9-dimensional parameter space of nonspinning binary neutron star inspirals can be sped up by a factor of ∼30 for the early advanced detectors' configurations (with sensitivities down to around 40 Hz) and ∼70 for sensitivities down to around 20 Hz. This speedup will increase to about 150 as the detectors improve their low-frequency limit to 10 Hz, reducing to hours analyses which could otherwise take months to complete. Although these results focus on interferometric gravitational wave detectors, the techniques are broadly applicable to any experiment where fast Bayesian analysis is desirable. [ABSTRACT FROM AUTHOR]

Many relevant applications in gravitational wave physics share a significant common problem: the seven-dimensional parameter space of gravitational waveforms from precessing compact binary inspirals and coalescences is large enough to prohibit covering the space of waveforms with sufficient density. We find that by using the reduced basis method together with a parametrization of waveforms based on their phase and precession, we can construct ultracompact yet high-accuracy representations of this large space. As a demonstration, we show that less than 100 judiciously chosen precessing inspiral waveforms are needed for 200 cycles, mass ratios from 1 to 10, and spin magnitudes < 0.9. In fact, using only the first 10 reduced basis waveforms yields a maximum mismatch of 0.016 over the whole range of considered parameters. We test whether the parameters selected from the inspiral regime result in an accurate reduced basis when including merger and ringdown; we find that this is indeed the case in the context of a nonprecessing effective-one-body model. This evidence suggests that as few as ~100 numerical simulations of binary black hole coalescences may accurately represent the seven-dimensional parameter space of precession waveforms for the considered ranges. [ABSTRACT FROM AUTHOR]

We introduce a reduced basis approach as a new paradigm for modeling, representing and searching for gravitational waves. We construct waveform catalogs for nonspinning compact binary coalescences, and we find that for accuracies of 99% and 99.999% the method generates a factor of about 10-10(5) fewer templates than standard placement methods. The continuum of gravitational waves can be represented by a finite and comparatively compact basis. The method is robust under variations in the noise of detectors, implying that only a single catalog needs to be generated.