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

TL;DR

This paper introduces ISOKANN, a Koopman-inspired neural network framework that extracts collective variables and models effective dynamics to analyze metastable transitions in complex molecular systems.

Contribution

It integrates Koopman operator theory with neural networks and reduced modeling to accurately predict transition pathways and rates from simulation data.

Findings

Successfully reconstructs coarse-grained kinetics in benchmark potentials.

Accurately reproduces transition times across different barriers.

Provides a principled framework for computing transition pathways.

Abstract

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.