Emulators for scarce and noisy data: Application to auxiliary field diffusion Monte Carlo for the deuteron
Rahul Somasundaram (Department of Physics, Syracuse University, Syracuse, NY 13244, USA, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA)
; Cassandra L. Armstrong (Intelligence and Space Research Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA); Pablo Giuliani (Facility for Rare Isotope Beams, Michigan State University, East Lansing, MI 48824, USA, Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA); Kyle Godbey (Facility for Rare Isotope Beams, Michigan State University, East Lansing, MI 48824, USA); Stefano Gandolfi (Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA); et al - Show all 6 authors
The validation, verification, and uncertainty quantification of computationally expensive theoretical models of quantum many-body systems require the construction of fast and accurate emulators. In this work, we develop emulators for auxiliary field diffusion Monte Carlo (AFDMC), a powerful many-body method for nuclear systems. We introduce a reduced-basis method (RBM) emulator for AFDMC and study it in the simple case of the deuteron. Furthermore, we compare our RBM emulator with the recently proposed parametric matrix model (PMM) that combines elements of RBMs with machine learning. We contrast these two approaches with a traditional Gaussian Process emulator. All three emulators constructed here are based on a very limited set of 5 training points, as expected for realistic AFDMC calculations, but validated against exact solutions. We find that the PMM, with emulator errors of only and speed-up factors of , outperforms our implementation of the other two emulators when applied to AFDMC.
