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

Abstract: We introduce hp-greedy, a refinement approach for building gravitational wave surrogates as an extension of the standard reduced basis framework. Our proposal is data-driven, with a domain decomposition of the parameter space, local reduced basis, and a binary tree as the resulting structure, which are obtained in an automated way. When compared to the standard global reduced basis approach, the numerical simulations of our proposal show three salient features: i) representations of lower dimension with no loss of accuracy, ii) a significantly higher accuracy for a fixed maximum dimensionality of the basis, in some cases by orders of magnitude, and iii) results that depend on the reduced basis seed choice used by the refinement algorithm. We first illustrate the key parts of our approach with a toy model and then present a more realistic use case of gravitational waves emitted by the collision of two spinning, non-precessing black holes. We discuss performance aspects of hp-greedy, such as overfitting with respect to the depth of the tree structure, and other hyperparameter dependences. As two direct applications of the proposed hp-greedy refinement, we envision: i) a further acceleration of statistical inference, which might be complementary to focused reduced-order quadratures, and ii) the search of gravitational waves through clustering and nearest neighbors.