# Learning Multi-type heterogeneous interacting particle systems

arXiv: https://arxiv.org/abs/2602.03954 · HTML: https://mlsanity.com/paper/2602.03954/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 48 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 22 of 22)

- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis](https://mlsanity.com/paper/1704.00708/) (2017)
- [Statistical and Computational Guarantees of Lloyd's Algorithm and its Variants](https://mlsanity.com/paper/1612.02099/) (2016)
- [Nonparametric inference of interaction laws in systems of agents from trajectory data](https://mlsanity.com/paper/1812.06003/) (2018)
- [Convergence Analysis for Rectangular Matrix Completion Using Burer-Monteiro Factorization and Gradient Descent](https://mlsanity.com/paper/1605.07051/) (2016)
- [Learning Mean-Field Equations from Particle Data Using WSINDy](https://mlsanity.com/paper/2110.07756/) (2021)
- [Sharp Restricted Isometry Bounds for the Inexistence of Spurious Local Minima in Nonconvex Matrix Recovery](https://mlsanity.com/paper/1901.01631/) (2019)
- [Learning interaction kernels in heterogeneous systems of agents from multiple trajectories](https://mlsanity.com/paper/1910.04832/) (2019)
- [Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories](https://mlsanity.com/paper/2007.15174/) (2020)
- [Learning interaction kernels in mean-field equations of 1st-order systems of interacting particles](https://mlsanity.com/paper/2010.15694/) (2020)
- [Cutoff for exact recovery of Gaussian mixture models](https://mlsanity.com/paper/2001.01194/) (2020)
- [Identifiability of interaction kernels in mean-field equations of interacting particles](https://mlsanity.com/paper/2106.05565/) (2021)
- [Phase Retrieval Meets Statistical Learning Theory: A Flexible Convex Relaxation](https://mlsanity.com/paper/1610.04210/) (2016)
- [Randomly Initialized Alternating Least Squares: Fast Convergence for Matrix Sensing](https://mlsanity.com/paper/2204.11516/) (2022)
- [Learning Anisotropic Interaction Rules from Individual Trajectories in a Heterogeneous Cellular Population](https://mlsanity.com/paper/2204.14141/) (2022)
- [A stochastic version of Stein Variational Gradient Descent for efficient sampling](https://mlsanity.com/paper/1902.03394/) (2019)
- [Alternating minimization for generalized rank one matrix sensing: Sharp predictions from a random initialization](https://mlsanity.com/paper/2207.09660/) (2022)
- [Statistically Optimal K-means Clustering via Nonnegative Low-rank Semidefinite Programming](https://mlsanity.com/paper/2305.18436/) (2023)
- [Inferring networks from time series: a neural approach](https://mlsanity.com/paper/2303.18059/) (2023)
- [Learning Interaction Variables and Kernels from Observations of Agent-Based Systems](https://mlsanity.com/paper/2208.02758/) (2022)
- [Interacting Particle Systems on Networks: joint inference of the network and the interaction kernel](https://mlsanity.com/paper/2402.08412/) (2024)
- [Evolutionary game dynamics with environmental feedback in a network with two communities](https://mlsanity.com/paper/2404.17082/) (2024)

## Built on by (most cited first, 1 of 1)

- [Learning Interaction Kernels from Collective Steady States](https://mlsanity.com/paper/2609.12004/) (2026)

## Abstract (arXiv)

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.