Goal-Oriented Neural Network Surrogates for Gravitational Wave Models

Fast gravitational wave models are needed in order to solve the Bayesian inverse problem at the heart of LIGO data analysis. To get around computationally expensive solvers for Einstein's equations in numerical relativity, a broad array of surrogate models has been developed to make such analyses tractable. These models utilize physical approximations as well as data-driven approaches to create synthetic waveforms that can be compared to LIGO data. In this work, we build on recent developments in using neural networks to learn the morphology of a signal generated by more expensive gravitational wave models. We use proper orthogonal decomposition to find dimensionally reduced representations of gravitational wave signals, and we then train neural networks to learn coefficients in this reduced basis from binary black hole parameters such as mass and spin. Furthermore, we introduce known noise characteristics of the LIGO and Virgo detectors via the power spectral density (PSD), in order to guide the reduced basis construction to reflect the sensitive frequencies of the detections. This goal-oriented approach allows our models to perform better in the inverse problem, producing posteriors that match the high-fidelity reference better than similar models that don't incorporate PSD information, according to computed Jensen-Shannon distances. We demonstrate this improvement in simplified settings using training data generated by the PhenomX family of gravitational wave models.