  The present work concerns the transferability of coarse-grained (CG) modeling
in reproducing the dynamic properties of the reference atomistic systems across
a range of parameters. In particular, we focus on implicit-solvent CG modeling
of polymer solutions. The CG model is based on the generalized Langevin
equation, where the memory kernel plays the critical role in determining the
dynamics in all time scales. Thus, we propose methods for transfer learning of
memory kernels. The key ingredient of our methods is Gaussian process
regression. By integration with the model order reduction via proper orthogonal
decomposition and the active learning technique, the transfer learning can be
practically efficient and requires minimum training data. Through two example
polymer solution systems, we demonstrate the accuracy and efficiency of the
proposed transfer learning methods in the construction of transferable memory
kernels. The transferability allows for out-of-sample predictions, even in the
extrapolated domain of parameters. Built on the transferable memory kernels,
the CG models can reproduce the dynamic properties of polymers in all time
scales at different thermodynamic conditions (such as temperature and solvent
viscosity) and for different systems with varying concentrations and lengths of
polymers.
