Maximum Entropy Theory of Multiscale Coarse-Graining via Matching Thermodynamic Forces: Application to a Molecular Crystal (TATB)

The MSCG/FM (multiscale coarse-graining via force-matching)
approach
is an efficient supervised machine learning method to develop microscopically
informed coarse-grained (CG) models. We present a theory based on
the principle of maximum entropy (PME) enveloping the existing MSCG/FM
approaches. This theory views the MSCG/FM method as a special case
of matching the thermodynamic forces from the extended ensemble described
by the set of thermodynamic (relevant) system coordinates. This set
may include CG coordinates, the stress tensor, applied external fields,
and so forth, and may be characterized by nonequilibrium conditions.
Following the presentation of the theory, we discuss the consistent
matching of both bonded and nonbonded interactions. The proposed PME
formulation is used as a starting point to extend the MSCG/FM method
to the constant strain ensemble, which together with the explicit
matching of the bonded forces is better suited for coarse-graining
anisotropic media at a submolecular resolution. The theory is demonstrated
by performing the fine coarse-graining of crystalline 1,3,5-triamino-2,4,6-trinitrobenzene
(TATB), a well-known insensitive molecular energetic material, which
exhibits highly anisotropic mechanical properties.