Learning Multi-type heterogeneous interacting particle systems

TL;DR

This paper introduces a three-stage framework for inferring network topology, interaction types, and parameters in heterogeneous particle systems from trajectory data, combining matrix sensing, clustering, and factorization.

Contribution

It presents a novel approach with theoretical guarantees for joint inference in complex multi-type interacting particle systems from multi-trajectory data.

Findings

Accurate reconstruction of system dynamics in synthetic experiments.

Robustness to noise demonstrated in numerical simulations.

Theoretical bounds established for estimation error and type recovery.

Abstract

We propose a framework for the joint inference of network topology, multi-type interaction kernels, and latent type assignments in heterogeneous interacting particle systems from multi-trajectory data. This learning task is a challenging non-convex mixed-integer optimization problem, which we address through a novel three-stage approach. First, we leverage shared structure across agent interactions to recover a low-rank embedding of the system parameters via matrix sensing. Second, we identify discrete interaction types by clustering within the learned embedding. Third, we recover the network weight matrix and kernel coefficients through matrix factorization and a post-processing refinement. We provide theoretical guarantees with estimation error bounds under a Restricted Isometry Property (RIP) assumption and establish conditions for the exact recovery of interaction types based on cluster separability. Numerical experiments on synthetic datasets, including heterogeneous predator-prey systems, demonstrate that our method yields an accurate reconstruction of the underlying dynamics and is robust to noise.