Large-scale computational molecular models provide scientists
a
means to investigate the effect of microscopic details on emergent
mesoscopic behavior. Elucidating the relationship between variations
on the molecular scale and macroscopic observable properties facilitates
an understanding of the molecular interactions driving the properties
of real world materials and complex systems (e.g., those found in
biology, chemistry, and materials science). As a result, discovering
an explicit, systematic connection between microscopic nature and
emergent mesoscopic behavior is a fundamental goal for this type of
investigation. The molecular forces critical to driving the behavior
of complex heterogeneous systems are often unclear. More problematically,
simulations of representative model systems are often prohibitively
expensive from both spatial and temporal perspectives, impeding straightforward
investigations over possible hypotheses characterizing molecular behavior.
While the reduction in resolution of a study, such as moving from
an atomistic simulation to that of the resolution of large coarse-grained
(CG) groups of atoms, can partially ameliorate the cost of individual
simulations, the relationship between the proposed microscopic details
and this intermediate resolution is nontrivial and presents new obstacles
to study. Small portions of these complex systems can be realistically
simulated. Alone, these smaller simulations likely do not provide
insight into collectively emergent behavior. However, by proposing
that the driving forces in both smaller and larger systems (containing
many related copies of the smaller system) have an explicit connection,
systematic bottom-up CG techniques can be used to transfer CG hypotheses
discovered using a smaller scale system to a larger system of primary
interest. The proposed connection between different CG systems is
prescribed by (i) the CG representation (mapping) and (ii) the functional
form and parameters used to represent the CG energetics, which approximate
potentials of mean force (PMFs). As a result, the design of CG methods
that facilitate a variety of physically relevant representations,
approximations, and force fields is critical to moving the frontier
of systematic CG forward. Crucially, the proposed connection between
the system used for parametrization and the system of interest is
orthogonal to the optimization used to approximate the potential of
mean force present in all systematic CG methods. The empirical efficacy
of machine learning techniques on a variety of tasks provides strong
motivation to consider these approaches for approximating the PMF
and analyzing these approximations.