Ensuring thermodynamic consistency with invertible coarse-graining

• Published in: The Journal of chemical physics Vol. 158; no. 12; p. 124126
• Main Authors: Chennakesavalu, Shriram, Toomer, David J, Rotskoff, Grant M
• Format: Journal Article
• Language: English
• Published: United States 28.03.2023
• ISSN: 1089-7690
• DOI: 10.1063/5.0141888

Coarse-grained models are a core computational tool in theoretical chemistry and biophysics. A judicious choice of a coarse-grained model can yield physical insights by isolating the essential degrees of freedom that dictate the thermodynamic properties of a complex, condensed-phase system. The reduced complexity of the model typically leads to lower computational costs and more efficient sampling compared with atomistic models. Designing "good" coarse-grained models is an art. Generally, the mapping from fine-grained configurations to coarse-grained configurations itself is not optimized in any way; instead, the energy function associated with the mapped configurations is. In this work, we explore the consequences of optimizing the coarse-grained representation alongside its potential energy function. We use a graph machine learning framework to embed atomic configurations into a low-dimensional space to produce efficient representations of the original molecular system. Because the representation we obtain is no longer directly interpretable as a real-space representation of the atomic coordinates, we also introduce an inversion process and an associated thermodynamic consistency relation that allows us to rigorously sample fine-grained configurations conditioned on the coarse-grained sampling. We show that this technique is robust, recovering the first two moments of the distribution of several observables in proteins such as chignolin and alanine dipeptide.