Learning Multi-type heterogeneous interacting particle systems

2026-02-03

AI Summary

This study addresses the joint inference of network topology, multi-type interaction kernels, and latent particle types in heterogeneous interacting particle systems from multiple trajectory data. To this end, the authors propose a three-stage method: first obtaining a low-rank embedding of system parameters via matrix sensing, then clustering in the embedding space to identify discrete interaction types, and finally recovering network weights and kernel coefficients through matrix factorization combined with post-processing. This approach is the first to enable joint learning of network structure, interaction kernels, and type labels in heterogeneous particle systems, and provides theoretical error bounds and conditions for exact type recovery under the restricted isometry property (RIP) assumption. Experiments demonstrate that the method accurately reconstructs dynamical structures in synthetic datasets—such as heterogeneous predator-prey systems—and exhibits strong robustness to noise.

Technology Category

• Machine Learning: Kernel Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Multiagent Systems: Multiagent Learning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• heterogeneous interacting particle systems
• network topology inference
• multi-type interaction kernels
• latent type assignment
• multi-trajectory data

Innovation

• heterogeneous interacting particle systems
• multi-type interaction kernels
• low-rank embedding
• matrix sensing
• cluster separability