# Black Hole Perturbation Theory

High-accuracy gravitational-wave source modeling has long avoided machine learning because neural networks carry a noise floor. Researchers trained a graph neural network as a preconditioner for an iterative solver, leaving the traditional GMRES to enforce final accuracy while the network only accelerates convergence. On the high-frequency elliptic equations for asymmetric-mass black hole binaries, the hardest parameter regions need 2 to 15 fewer GMRES iterations than basic ILU and 2 to 4 times less wall time than the next best method.

High-accuracy gravitational-wave source modeling has long avoided machine learning because neural networks carry a noise floor. Researchers trained a graph neural network as a preconditioner for an iterative solver, leaving the traditional GMRES to enforce final accuracy while the network only accelerates convergence. On the high-frequency elliptic equations for asymmetric-mass black hole binaries, the hardest parameter regions need 2 to 15 fewer GMRES iterations than basic ILU and 2 to 4 times less wall time than the next best method.