Structural Coarse-Graining via Multi-Objective Optimization with Differentiable Simulation

In the realm of multiscale molecular simulations, structure-based coarse graining is a prominent approach for creating efficient coarse-grained (CG) representations of soft matter systems such as polymers. This involves optimizing CG interactions by matching static correlation functions of corresponding degrees of freedom in all-atom (AA) models. Here, we present a versatile method, namely, differentiable coarse-graining (DiffCG), which combines multi-objective optimization and differentiable simulation. The DiffCG approach is capable of constructing robust CG models by iteratively optimizing effective potentials to simultaneously match multiple target properties. We demonstrate our approach by concurrently optimizing bonded and non-bonded potentials of a CG model of polystyrene (PS) melts. The resulting CG-PS model accurately reproduces both structural and thermodynamic properties of the AA counterpart. More importantly, leveraging the multi-objective optimization capability, we develop a precise and efficient CG model for PS melts that is transferable across a wide range of temperatures, i.e., from $400$ to $600$ K. It is achieved via optimizing a pairwise potential with nonlinear temperature dependence in the CG model to simultaneously match target data from AA-MD simulations at multiple thermodynamic states. Our work showcases a promising route for developing accurate and transferable CG models of complex soft-matter systems through multi-objective optimization with differentiable simulation.