Reduced Order and Surrogate Models for Gravitational Waves

Abstract

We present an introduction to some of the state of the art in reduced order and surrogate modeling in gravitational wave (GW) science. Approaches that we cover include Principal Component Analysis, Proper Orthogonal Decomposition, the Reduced Basis approach, the Empirical Interpolation Method, Reduced Order Quadratures, and Compressed Likelihood evaluations. We divide the review into three parts: representation/compression of known data, predictive models, and data analysis. The targeted audience is that one of practitioners in GW science, a field in which building predictive models and data analysis tools that are both accurate and fast to evaluate, especially when dealing with large amounts of data and intensive computations, are necessary yet can be challenging. As such, practical presentations and, sometimes, heuristic approaches are here preferred over rigor when the latter is not available. This review aims to be self-contained, within reasonable page limits, with little previous knowledge (at the undergraduate level) requirements in mathematics, scientific computing, and other disciplines. Emphasis is placed on optimality, as well as the curse of dimensionality and approaches that might have the promise of beating it. We also review most of the state of the art of GW surrogates. Some numerical algorithms, conditioning details, scalability, parallelization and other practical points are discussed. The approaches presented are to large extent non-intrusive and data-driven and can therefore be applicable to other disciplines. We close with open challenges in high dimension surrogates, which are not unique to GW science.

Gravitational wave surrogates through automated machine learning

“…A RB-EIM surrogate built in [13] following the prescriptions described in the previous section, from those 22 NR simulations, using polynomial least squares for the regression step. The model agrees after a simulationdependent time shift and physical rotation with the full NR results within numerical truncation errors with the advantage of being fast to evaluate for any value of q ∈ [1,10]. We refer to the associated waveforms as polynomial least-squares or least-squares (for short) waveforms, and denote any of them as h LS .…”

“…Figure5shows a comparison between the model resulting from BP 1 and NR waveform (plus polarization), for q = 4.499. This is one of the 22 NR values, close to the center of the interval used for q:[1,10].…”

“…Construction of real-time or near real-time gravitational wave surrogates based on a small but carefully selected set of known waveforms has over the last years become a discipline on itself in gravitational wave (GW) science, for a review see [1]. These surrogates are based on a fiducial or underlying model, which can be obtained from full numerical relativity (NR) solutions to the Einstein equations or physical approximants such as Effective One Body (EOB), Phenomenological (Phenom) or Post-Newtonian (PN) ones, as physical examples.…”

“…Appendix A: Blueprints used List of the 87 blueprints used in this study, ranked from smallest to largest error max q∈ [1,10] E(q) with E(q) defined by Equation (6).…”

Testing gravitational waveform models using angular momentum

“…Finally there is the family of surrogate waveform models [31,[54][55][56][57], from which we use the NRSur7dq4 [31] model. See [58] for a review.…”