# Reactive Flux Matching: Mechanism Discovery and Adaptive Sampling of Rare Events

arXiv: https://arxiv.org/abs/2606.06295 · HTML: https://mlsanity.com/paper/2606.06295/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 55 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Builds on (most cited first, 12 of 12)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Benchmarking Graphormer on Large-Scale Molecular Modeling Datasets](https://mlsanity.com/paper/2203.04810/) (2022)
- [OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentials](https://mlsanity.com/paper/2310.03121/) (2023)
- [Solving for high dimensional committor functions using artificial neural networks](https://mlsanity.com/paper/1802.10275/) (2018)
- [Computing Committor Functions for the Study of Rare Events Using Deep Learning](https://mlsanity.com/paper/1906.06285/) (2019)
- [Deep learning probability flows and entropy production rates in active matter](https://mlsanity.com/paper/2309.12991/) (2023)
- [Deep Learning Method for Computing Committor Functions with Adaptive Sampling](https://mlsanity.com/paper/2404.06206/) (2024)
- [Rare Event Analysis via Stochastic Optimal Control](https://mlsanity.com/paper/2604.13213/) (2026)
- [Model-free learning of probability flows: Elucidating the nonequilibrium dynamics of flocking](https://mlsanity.com/paper/2411.14317/) (2024)

## Abstract (arXiv)

Path sampling methods generate ensembles of reactive trajectories connecting metastable states, but extracting mechanistic insight from these data remains nontrivial. We introduce Flux Matching, a framework that learns two complementary objects directly from reactive trajectory data: a current velocity u(z), whose streamlines trace the dominant reaction pathways, and a scalar potential h(z), obtained from a weighted Helmholtz-Hodge decomposition of the reactive current, that serves as a data-driven reaction coordinate. Both minimize quadratic functionals over the reactive path ensemble, analogous to the flow matching loss in generative modeling, and require no knowledge of the underlying dynamics or stationary distribution. Unlike committor-based methods, u and h remain well-defined under projection onto non-Markovian collective variables, and their level sets in turn provide adaptive interfaces for improved sampling with enhanced sampling methods. Flux Matching is validated through the generation of current velocity trajectories and rate constant calculations on molecular systems.