Factorization in molecular modeling and belief propagation algorithms

Area of Science:

• Computational physics
• Statistical machine learning
• Computational chemistry

Background:

• Factorization is crucial for reducing computational complexity in high-dimensional systems.
• Molecular modeling uses approximate factorization for interactions, while machine learning employs belief propagation algorithms.
• These fields have developed factorization methods independently.

Purpose of the Study:

• To bridge the gap between factorization algorithms in molecular modeling and machine learning.
• To highlight the common foundation of probability distribution factorization.
• To encourage cross-disciplinary development of advanced factorization techniques.

Main Methods:

• Review of conventional molecular modeling techniques (e.g., molecular dynamics, Monte Carlo).
• Introduction of local distribution theory for factorizing molecular system distributions.
• Discussion of belief propagation and loopy belief propagation algorithms.

Main Results:

• Identified factorization of probability distributions as a unifying concept.
• Presented connections and differences between molecular modeling and machine learning factorization approaches.
• Highlighted the independent development trajectories of these algorithms.

Conclusions:

• Further development of factorization algorithms can benefit physical modeling of complex molecular systems.
• Cross-pollination of ideas between machine learning and molecular modeling is encouraged.
• This perspective aims to stimulate novel research at the intersection of these fields.