This program will bring together experts across gravitational physics to address one of the central challenges of the coming decade: modelling gravitational waves with the precision required by next-generation observatories. As LIGO, Virgo, and KAGRA are upgraded, and as LISA, the Einstein Telescope, and Cosmic Explorer come online, gravitational-wave observations will become dramatically more sensitive. Extracting the full physics from these signals will require equally precise theoretical waveform models. Achieving this demands tools spanning perturbative methods, quantum-field-theory-inspired calculations, and large-scale numerical simulations, approaches that have achieved major successes but have largely developed in isolation.

The program will bring together four key communities: black hole perturbation theory, which probes strong-field dynamics and ringdown; scattering amplitudes and effective field theory, which have produced high-order results for binary dynamics; numerical relativity, which provides fully nonlinear benchmarks; and data analysis, which tests theoretical predictions against observations. The goal is to develop waveform models spanning the full inspiral-merger-ringdown process, with systematic improvements and quantified uncertainties. Recent progress at the interfaces between these areas, including links between post-Minkowskian theory, numerical simulations, and perturbative ringdown calculations, makes this an especially timely effort.