Many-Body Neural Network-Based Force Field for Structure-Based Coarse-Graining of Water

High-fidelity results from atomistic simulations can only be obtained by using accurate force-field (FF) parameters. Although empirical FFs are commonly used in the modeling of atomistic systems due to their simplicity, they have many limitations inherent in the crude approximations associated with their analytical form. Recent advances in neural network-based FFs have led to more accurate FFs by using symmetry functions or full many-body expansions. However, this approach leads to several issues including the arbitrariness of the symmetry functions, and the intangible and uninterpretable interactions which are only known once the positions of all atoms are set. More importantly, training is another bottleneck, as high-quality force and energy information is required, which is usually not accessible from experimental data. To solve these issues within the context of structure-based coarse-graining methods, we switch in this work to a local-search method to target the reference structure instead of using conventional backpropagation algorithms used to target the forces and energies of the reference structure. Our FF is decomposed into two-, three-, and higher-order terms, where each term is modeled with a separate neural network. To show the versatility of our method, we study four different systems, namely, Stillinger-Weber particles as an atomistic case and three water models, namely SPC/E, MB-pol, and ab initio, as coarse-graining cases. We show the successful application of our approach, by reproducing structural properties of different water models, followed by providing insight into the role of two-and three-body interactions. The results of all models indicate that the double-well isotropic pair potential, the signature of water-like behavior in an isotropic system, vanishes upon inclusion of the three-body interaction, showing dominance of the three-body interaction over the two-body interaction in water-like behavior with the single-well isotropic pair potential.