Neural Green’s function for Laplacian systems

Solving linear system of equations stemming from Laplacian operators is at the heart a wide range applications. Due to sparsity systems, iterative solvers such as Conjugate Gradient and Multigrid are usually employed when solution has large number degrees freedom. These can be seen sparse approximations Green’s function for operator. In this paper we propose machine learning approach that regresses boundary conditions. This enabled by effectively represented in multi-scale fashion, drastically reducing cost associated with dense matrix representation. Additionally, since solely dependent on conditions, training proposed neural network does not require sampling right-hand side system. We show results our method outperforms state art methods.