Surrogate waveform models for binary black holes

Understanding the exact shape of the gravitational-wave signal produced when two black holes spiral together and merge is fundamental to almost every aspect of gravitational-wave astronomy. Waveform models are needed to detect signals in noisy detector data, to measure the masses and spins of the colliding objects, and to test whether Einstein’s general relativity correctly predicts the dynamics of strongly-gravitating systems.

The most accurate waveforms come from numerical relativity (NR): directly solving Einstein’s field equations on a supercomputer. A single NR waveform can take days or weeks to produce, and covers only a narrow slice of the parameter space of possible black hole masses and spins.

This bottleneck matters enormously for Bayesian parameter estimation, which requires evaluating tens of millions of trial waveforms to characterise a single gravitational-wave event. The heron project addresses this challenge by building surrogate models — fast, data-driven approximations trained on sets of NR waveforms.

Unlike many surrogate approaches, heron uses Gaussian process regression, which provides not only a fast waveform prediction but also a principled uncertainty estimate. This uncertainty reflects the regions of parameter space where the training data are sparse and the model is extrapolating. These uncertainties can be propagated forward into parameter estimation, allowing the analysis to account for waveform model error directly in inference.

Quantifying and marginalising over waveform uncertainty has important implications for tests of general relativity. Systematic model error can otherwise masquerade as a departure from GR, and accounting for it properly becomes increasingly important as detectors grow more sensitive and signal characterisation becomes more precise.