IMSRG-Net: A machine learning-based solver for In-Medium Similarity Renormalization Group

We present a novel method, IMSRG-Net, which utilizes machine learning techniques as a solver for the in-medium Similarity Renormalization Group (IMSRG). The primary objective of IMSRG-Net is to approximate the Magnus operators $\Omega(s)$ in the IMSRG flow equation, thereby offering an alternative to the computationally intensive part of IMSRG calculations. The key idea of IMSRG-Net is its design of the loss function inspired by physics-informed neural networks to encode the underlying {\it physics}, i.e., IMSRG flow equation, into the model. Through training on a dataset comprising ten data points with flow parameters up to $s = 20$, capturing approximately one-eighth to one-quarter of the entire flow, IMSRG-Net exhibits remarkable accuracy in extrapolating the ground state energies and charge radii of ${}^{16}$O and ${}^{40}$Ca. Furthermore, this model demonstrates effectiveness in deriving effective interactions for a valence space.