Training and Projecting: A Reduced Basis Method Emulator for Many-Body Physics

We present the reduced basis method (RBM) as a tool for developing emulators for equations with tunable parameters within the context of the nuclear many-body problem. The RBM uses a basis expansion informed by a set of solutions for a few values of the model parameters and then projects the equations over a well-chosen low-dimensional subspace. We connected some of the results in the eigenvector continuation literature to the formalism of RBMs and show how RBMs can be applied to a broader set of problems. We applied the RBM to the one-dimensional Gross-Pitaevskii equation with a harmonic trapping potential and to nuclear density functional theory for 48Ca. The outstanding performance of the approach, together with its straightforward implementation, show promise for its application to the emulation of computationally demanding calculations, including uncertainty quantification.