As it is well-known, eigenpair calculations for large systems can get very expensive. At least, after taking the type of application into consideration, is it feasible to find a "shape" for something like an abstract subspace in which the eigenvectors for a certain amount of smallest eigenvalues live in? Could this be done in way of finding a relevant mapping, metric, or parametrization?
I am thinking about using Graph Neural Networks to extract useful structural information of molecules and feed it into a sort of subspace regression algorithm for the purpose of speeding up Density Functional Theory calculations.
EDIT: Clarified that the problem doesn't involve finding all eigenpairs of a system, i.e., a certain amount corresponding to the smallest eigenvalues.
My question may have been ill-posed. I believe what would be appropriate is to use a vector or directional regression based off of molecular structure instead of a subspace regression, for example.
Thanks to Paul Sinclair for reinforcing some technicalities.