  Partial differential equations (PDEs) are widely used across the physical and
computational sciences. Decades of research and engineering went into designing
fast iterative solution methods. Existing solvers are general purpose, but may
be sub-optimal for specific classes of problems. In contrast to existing
hand-crafted solutions, we propose an approach to learn a fast iterative solver
tailored to a specific domain. We achieve this goal by learning to modify the
updates of an existing solver using a deep neural network. Crucially, our
approach is proven to preserve strong correctness and convergence guarantees.
After training on a single geometry, our model generalizes to a wide variety of
geometries and boundary conditions, and achieves 2-3 times speedup compared to
state-of-the-art solvers.
