# Effective Dynamics and Transition Pathways from Koopman-Inspired Neural Learning of Collective Variables

arXiv: https://arxiv.org/abs/2604.05778 · HTML: https://mlsanity.com/paper/2604.05778/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 46 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## Builds on (most cited first, 5 of 5)

- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks](https://mlsanity.com/paper/2110.14523/) (2021)
- [Reaction coordinate flows for model reduction of molecular kinetics](https://mlsanity.com/paper/2309.05878/) (2023)
- [On finding optimal collective variables for complex systems by minimizing the deviation between effective and full dynamics](https://mlsanity.com/paper/2405.02001/) (2024)
- [Understanding recent deep-learning techniques for identifying collective variables of molecular dynamics](https://mlsanity.com/paper/2307.00365/) (2023)

## Abstract (arXiv)

The ISOKANN (Invariant Subspaces of Koopman Operators Learned by Artificial Neural Networks) framework provides a data-driven route to extract collective variables (CVs) and effective dynamics from complex molecular systems. In this work, we integrate the theoretical foundation of Koopman operators with Krylov-like subspace algorithms, and reduced dynamical modeling to build a coherent picture of how to describe metastable transitions in high-dimensional systems based on CVs. Starting from the identification of CVs based on dominant invariant subspaces, we derive the corresponding effective dynamics on the latent space and connect these to transition rates and times, committor functions, and transition pathways. The combination of Koopman-based learning and reduced-dimensional effective dynamics yields a principled framework for computing transition rates and pathways from simulation data. Numerical experiments on one-, two-, and three-dimensional benchmark potentials illustrate the ability of ISOKANN to reconstruct the coarse-grained kinetics and reproduce transition times across enthalpic and entropic barriers.