# Flow Matching for Optimal Reaction Coordinates of Biomolecular System

arXiv: https://arxiv.org/abs/2408.17139 · HTML: https://mlsanity.com/paper/2408.17139/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 10 of its 46 references that are in the map.
- First posted on arXiv 30 Aug 2024.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 10 of 10)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Variational approach for learning Markov processes from time series data](https://mlsanity.com/paper/1707.04659/) (2017)
- [Deeptime: a Python library for machine learning dynamical models from time series data](https://mlsanity.com/paper/2110.15013/) (2021)
- [Variational Koopman models: slow collective variables and molecular kinetics from short off-equilibrium simulations](https://mlsanity.com/paper/1610.06773/) (2016)
- [Nonlinear Discovery of Slow Molecular Modes using State-Free Reversible VAMPnets](https://mlsanity.com/paper/1902.03336/) (2019)
- [High-resolution Markov state models for the dynamics of Trp-cage miniprotein constructed over slow folding modes identified by state-free reversible VAMPnets](https://mlsanity.com/paper/1906.04890/) (2019)
- [Reaction coordinate flows for model reduction of molecular kinetics](https://mlsanity.com/paper/2309.05878/) (2023)
- [From latent dynamics to meaningful representations](https://mlsanity.com/paper/2209.00905/) (2022)

## Built on by (most cited first, 2 of 2)

- [Enhanced Sampling for Efficient Learning of Coarse-Grained Machine Learning Potentials](https://mlsanity.com/paper/2510.11148/) (2025)
- [Coarse-Grained Boltzmann Generators](https://mlsanity.com/paper/2602.10637/) (2026)

## Abstract (arXiv)

We present flow matching for reaction coordinates (FMRC), a novel deep learning algorithm designed to identify optimal reaction coordinates (RC) in biomolecular reversible dynamics. FMRC is based on the mathematical principles of lumpability and decomposability, which we reformulate into a conditional probability framework for efficient data-driven optimization using deep generative models. While FMRC does not explicitly learn the well-established transfer operator or its eigenfunctions, it can effectively encode the dynamics of leading eigenfunctions of the system transfer operator into its low-dimensional RC space. We further quantitatively compare its performance with several state-of-the-art algorithms by evaluating the quality of Markov state models (MSM) constructed in their respective RC spaces, demonstrating the superiority of FMRC in three increasingly complex biomolecular systems. In addition, we successfully demonstrated the efficacy of FMRC for bias deposition in the enhanced sampling of a simple model system. Finally, we discuss its potential applications in downstream applications such as enhanced sampling methods and MSM construction.