Training and Projecting: A Reduced Basis Method Emulator for Many-Body Physics
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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 connect some of the results in the eigenvector continuation literature to the formalism of RBMs and show how RBMs can be applied to a broad set of problems. As we illustrate, the possible success of the RBM on such problems can be diagnosed beforehand by a principal component analysis. We apply 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.
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