Systematic selection of symmetry functions for transferable neural network potentials in coarse-grained molecular modeling

Developing transferable coarse-grained (CG) models is a major challenge in molecular simulations, as conventional potentials are often state-point and system composition dependent. While neural network (NN) potentials offer a promising path to transferability, their development is hampered by training instabilities and the complex, often heuristic, selection of model parameters. This work presents a systematic methodology to address these issues, focusing on the rational selection of descriptors for NN-based CG potentials. We propose a systematic workflow for parameterizing Behler-Parrinello symmetry functions (G2) by analyzing their resolving power and response to changes in system conditions, such as concentration. This allows for the selection of an optimized set of descriptors that captures essential structural features, handles short-range repulsions efficiently, and includes descriptors sensitive to the thermodynamic state to ensure transferability. Furthermore, we adopt a network extension technique that enables iterative improvement of model accuracy by expanding the network architecture and descriptor set without discarding prior training. The methodology is demonstrated on a CG model of methanol-water mixtures, with the NN trained to reproduce radial distribution functions derived from atomistic simulations across a wide range of methanol concentrations (10%-100%). The resulting NN potential, built using the systematic approach, demonstrates significantly improved accuracy and transferability, particularly at high concentrations, outperforming models developed previously with empirically chosen parameters. Our findings provide practical guidelines and a robust workflow for developing accurate and transferable NN potentials for CG simulations, paving the way for more reliable mesoscale modeling of complex systems.