@article { , title = {Systematic derivation of hybrid coarse-grained models}, abstract = {Molecular dynamics represents a key enabling technology for applications ranging from biology to the development of new materials. However, many real-world applications remain inaccessible to fully-resolved simulations due their unsustainable computational costs and must therefore rely on semi-empirical coarse-grained models. Significant efforts have been devoted in the last decade towards improving the predictivity of these coarse-grained models and providing a rigorous justification of their use, through a combination of theoretical studies and data-driven approaches. One of the most promising research effort is the (re)discovery of the Mori-Zwanzig projection as a generic, yet systematic, theoretical tool for deriving coarse-grained models. Despite its clean mathematical formulation and generality, there are still many open questions about its applicability and assumptions. In this work, we propose a detailed derivation of a hybrid multi-scale system, generalising and further investigating the approach developed in [EspaƱol, P., EPL, 88, 40008 (2009)]. Issues such as the general coexistence of atoms (fully-resolved degrees of freedom) and beads (larger coarse-grained units), the role of the fine-to-coarse mapping chosen, and the approximation of effective potentials are discussed. The theoretical discussion is supported by numerical simulations of a monodimen-sional nonlinear periodic benchmark system with an open-source parallel Julia code, easily extensible to arbitrary potential models and fine-to-coarse mapping functions. The results presented highlight the importance of introducing, in the macroscopic model, non-constant fluctuating and dissipative terms, given by the Mori-Zwanzig approach, to correctly reproduce the reference fine-grained results, without requiring ad-hoc calibration of interaction potentials and thermostats.}, doi = {10.1103/PhysRevE.99.013303}, eissn = {1550-2376}, issn = {2470-0045}, issue = {1}, journal = {Physical Review E}, note = {29 pages, 9 figures}, publicationstatus = {Published}, publisher = {American Physical Society}, url = {https://nottingham-repository.worktribe.com/output/1449043}, volume = {99}, keyword = {Chemical Physics}, year = {2019}, author = {Di Pasquale, Nicodemo and Hudson, Thomas and Icardi, Matteo} }