Data-driven Reduction of Transfer Operators for Particle Clustering Dynamics

TL;DR

This paper introduces a data-driven operator-based method to simplify and analyze particle clustering dynamics, capturing key features and transition pathways efficiently.

Contribution

It presents a novel framework that reduces transfer operators for particle systems, enabling interpretable analysis of clustering and metastability from simulation data.

Findings

Reduced models accurately reproduce clustering behavior.

Spectral analysis reveals dominant transition pathways.

Method captures metastable states and transition times.

Abstract

We develop an operator-based framework to coarse-grain interacting particle systems that exhibit clustering dynamics. Starting from the particle-based transfer operator, we first construct a sequence of reduced representations: the operator is projected onto concentrations and then further reduced by representing the concentration dynamics on a geometric low-dimensional manifold and an adapted finite-state discretization. The resulting coarse-grained transfer operator is finally estimated from dynamical simulation data by inferring the transition probabilities between the Markov states. Applied to systems with multichromatic and Morse interaction potentials, the reduced model reproduces key features of the clustering process, including transitions between cluster configurations and the emergence of metastable states. Spectral analysis and transition-path analysis of the estimated operator reveal implied time scales and dominant transition pathways, providing an interpretable and efficient description of particle-clustering dynamics.