The new field of gravitational wave science is a multidisciplinary subject, engaging and enriching many different research areas. Yet, the associated computational challenges are enormous. The programme will initiate an exchange of ideas and partnership between a diverse group of scientists, unified in the pursuit of gravitational wave physics. By incorporating perspectives from multiple communities, including astrophysicists, cosmologists and relativists together with amplitudes-focused theorists and particle physicists, we expect to chart a course towards extracting foundational physics from gravitational wave observations in the years to come.