Reduced Order Modeling and Gravitational Waves

I will give an overview of a program to map the space of configurations of binary compact coalescences, starting for preliminary indications a couple of years ago that the problem is amenable to reduced order modeling. I will then give an overview of Reduced Basis, our results obtained so far and a roadmap for the future.  Essentially, the core issue is how to chose the most relevant points in parameter space, in a nearly optimal way, and to select which configurations are "the most representative ones". This applies to the case in which the emitted gravitational waves can be simply evaluated using closed form approximations or obtained by solving simple equations but, most important, when deciding which configurations to solve for in numerical simulations of the full Einstein equations. I will also discuss ongoing work and the challenges associated with interpolating between high accuracy between the reduced basis solutions.  We have so far found that the representation error of the reduced basis decays exponentially with the number of elements in the basis, providing dramatic savings compared to traditional methods.