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 (singular value) decompositions, 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 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 related 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 a large extent non-intrusive (in the sense that no differential equations are invoked) 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.

An automated parameter domain decomposition approach for gravitational wave surrogates using hp-greedy refinement

“…the minimum over the coefficients {c i,λ }, turns to be a least squares one for those coefficients. There is a unique solution to this problem: it is the orthogonal projection P n with respect to the scalar product (3) to the span of the reduced basis [21]. The n-width then takes the form…”

“…Therefore, computationally cheaper approaches become attractive. An effective one is through a greedy algorithm, which is quasi-optimal in a precise mathematical sense, highly parallelizable, and of linear complexity; for more details see [21].…”

“…The use of the RBM [9][10][11][12][13] has been largely adopted in GW science [14][15][16][17][18][19][20], both for building surrogate models and for statistical inference, significantly reducing the associated computational costs while retaining high accuracy-see [21] for a review. Existing approaches in this application domain have normally used a global basis, similar in spirit to spectral methods.…”

Numerical relativity for Horndeski gravity

“…We can then write the spacetime metric h Surrogate modeling of gravitational waveforms also shows that gravitational waveforms for a variety of gravitational wave sources can be accurately described using a relatively small number of parameters. 151 as…”

Merging Black Holes: Assessing the Performance of Two Analytic Gravitational Waves Models

“…It is also very useful, because it allows us to employ approximate functions that are much simpler to work with, but contain the physical information we need to a high degree of accuracy, to quickly generate GW templates. Indeed, analytical models are easy to generate, are not plagued by numerical errors inherent to computer simulations [21] and do not rely on interpolation, inherent in the NR-based surrogate GW models [22]. Even so, analytical models do present the disadvantage that they are lengthy, cumbersome to build, and when it comes to the merger phase, they rely entirely on NR results to envelop the nonlinear physics of the collision, which becomes thus the least accurate part of those models, although it is the loudest signal in the detector.…”