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

Area of Science:

• Computational Chemistry
• Molecular Dynamics
• Statistical Mechanics

Background:

• Accurate coarse-grained models are crucial for simulating large molecular systems over extended length and time scales.
• Existing methods face challenges in controlling errors and systematic improvement.
• Fully atomic models are computationally expensive for large-scale simulations.

Purpose of the Study:

• To develop a broad theoretical framework for a novel coarse-graining approach based on relative entropy minimization.
• To establish numerical strategies for practical applications of this methodology.
• To demonstrate the effectiveness and error control of the relative entropy framework.

Main Methods:

• Variational minimization of the relative entropy (S(rel)) functional.
• Developing theoretical connections to existing coarse-graining methods (e.g., inverse Monte Carlo, force matching).
• Proposing new numerical minimization approaches and applying them to a model system.

Main Results:

• The relative entropy framework provides tight control over coarse-graining errors.
• A systematic approach to reducing these errors is suggested.
• Fundamental connections to other coarse-graining strategies are elucidated.
• New numerical strategies for minimization are presented.

Conclusions:

• The relative entropy method offers a robust and systematic way to generate accurate coarse-grained models.
• This framework enhances the modeling of complex molecular systems at large scales.
• The study provides a theoretical foundation and practical algorithms for improved coarse-graining.