Coarse-graining errors and numerical optimization using a relative entropy framework

2011/03/03 by Aviel Chaimovich, M. Scott Shell · 271 citations
Biochemistry, Genetics and Molecular Biology · Materials Science · Mathematics · #Advanced Electron Microscopy Techniques and Applications #Algorithm #Applied mathematics #Artificial intelligence #Block Copolymer Self-Assembly #Computer science #Energy minimization #Entropy (arrow of time) #Granularity #Inverse #Kullback–Leibler divergence #Machine Learning in Materials Science #Mathematical optimization #Mathematics #Minification #Monte Carlo method #Physics #Statistical physics #Statistics

paper · doi:10.1063/1.3557038

published in The Journal of Chemical Physics 134(9), 094112 (American Institute of Physics)

openalex publication_date 2011/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The ability to generate accurate coarse-grained models from reference fully atomic (or otherwise "first-principles") ones has become an important component in modeling the behavior of complex molecular systems with large length and time scales. We recently proposed a novel coarse-graining approach based upon variational minimization of a configuration-space functional called the relative entropy, S(rel), that measures the information lost upon coarse-graining. Here, we develop a broad theoretical framework for this methodology and numerical strategies for its use in practical coarse-graining settings. In particular, we show that the relative entropy offers tight control over the errors due to coarse-graining in arbitrary microscopic properties, and suggests a systematic approach to reducing them. We also describe fundamental connections between this optimization methodology and other coarse-graining strategies like inverse Monte Carlo, force matching, energy matching, and variational mean-field theory. We suggest several new numerical approaches to its minimization that provide new coarse-graining strategies. Finally, we demonstrate the application of these theoretical considerations and algorithms to a simple, instructive system and characterize convergence and errors within the relative entropy framework.

Citations

• On Information and Sufficiency
• The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models
• The relative entropy is fundamental to multiscale and inverse thermodynamic problems
• Multiscale coarse graining of liquid-state systems

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