  In computational materials science, coarse-graining approaches often lack a
priori uncertainty quantification (UQ) tools that estimate the accuracy of a
reduced-order model before it is calibrated or deployed. This is especially the
case in coarse-grained (CG) molecular dynamics (MD), where "bottom-up" methods
need to run expensive atomistic simulations as part of the calibration process.
As a result, scientists have been slow to adopt CG techniques in many settings
because they do not know in advance whether the cost of developing the CG model
is justified. To address this problem, we present an analytical method of
coarse-graining rigid-body systems that yields corresponding intermolecular
potentials with controllable levels of accuracy relative to their atomistic
counterparts. Critically, this analysis: (i) provides a mathematical foundation
for assessing the quality of a CG force field without running simulations, and
(ii) provides a tool for understanding how atomistic systems can be viewed as
appropriate limits of reduced-order models. Simulated results confirm the
validity of this approach at the trajectory level and point to issues that must
be addressed in coarse-graining fully non-rigid systems.
