This workshop aims to bring together researchers in solution-generating techniques and integrability, as well as Riemann-Hilbert factorization problems in gravity. It will also bring in expertise in AI and machine learning as a tool, especially in solving factorization problems, and in developing new matrix factorization methods that will be of service to solving gravitational PDEs. This event is the second workshop in a 4-month long BLH programme at the INI centred around the same topics.