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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]

We introduce a new approach for finding 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 Artificial 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% difference 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 field of GWs in particular and Artificial Intelligence in general. [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]