(Towards) Emulators for the In-Medium Similarity Renormalization Group

The in-medium similarity renormalization group (IMSRG) is an ab-initio method for computing the properties of medium mass and heavy nuclei. The IMSRG flow is a continuous unitary transformation which decouples a target reference state from all excitations in the many-body basis, thereby constructing a map to the true ground state (up to truncation errors).

We show that the solution to the IMSRG flow equation can be emulated via the data-driven discrete Koopman operator, effectively bypassing effort of solving the flow equation with standard ODE methods—at the cost of a few initial iterations of polynomial complexity. The Koopman operator characterizes a linear flow map which propagates a dynamical system. Evaluating the Koopman eigenfunctions, tuned by measurements of the flowing system, allows us to reproduce the system dynamics over a given range. Using this method, we construct a linear IMSRG transformation which emulates the conventional solution to a high degree of accuracy. We also apply a similar method to the parametric version of the IMSRG to allow sensitivity studies and uncertainty propagation for the parameters of the nuclear interactions.