# Molecular Flow Monte Carlo

## TL;DR

This paper introduces a novel continuous normalizing flow method for Monte Carlo molecular simulations that efficiently generates independent, low-energy configurations by transforming distributions based on two-body interactions, improving sampling efficiency.

## Contribution

It presents a new continuous normalizing flow approach tailored for molecular systems, enabling efficient sampling by avoiding high-energy states and improving proposal distributions.

## Key findings

- The inverse square flow effectively transforms distributions for molecular sampling.
- The method improves Metropolis-Hastings efficiency in simple molecular systems.
- It avoids extremely high energy configurations during sampling.

## Abstract

In this paper, we suggest a novel sampling method for Monte Carlo molecular simulations. In order to perform efficient sampling of molecular systems, it is advantageous to avoid extremely high energy configurations while also retaining the ability to quickly generate new and independent trial states. Thus, we introduce a continuous normalizing flow method which can quickly generate independent states for various proposal distributions using a first-order differential equation. We define this continuous normalizing molecular flow approach based on two-body intermolecular interactions to achieve a probability distribution transformation method which yields distributions which have probability densities of zero when molecule pairs are in close proximity; while in all other cases, the probability density is compressed such that it is spatial uniform. This transform provides the proposal distribution which generates no states of extremely high energy. We find that an inverse square flow is applicable as the continuous normalizing molecular flow. Using the transformed distribution, we can perform the Metropolis-Hastings method more efficiently. The high efficiency of the proposed method is demonstrated using simple molecular systems.