Who Drives the System? Classifying Mean-Field Particle Systems from Trajectory Data
Abstract
We study the supervised classification problem for interacting particle systems (IPS) from trajectory observations. The IPS belongs to one of K classes, each characterized by a distinct interaction drift. Given a learning dataset, the goal is then to predict the class label of a newly observed system based on the trajectory of a single particle. This setting raises several statistical challenges. First, the particles within each system interact and are therefore dependent. Second, although the full particle system is Markovian, the trajectory of a single particle is not. To address these difficulties, we exploit the McKean-Vlasov limit of the IPS, which describes the dynamics of a typical particle as the number of particles tends to infinity.
We propose a plug-in classification procedure based on estimating the interaction drift associated with each class from discretely observed trajectory data. Hence, for each class, we provide a new nonparametric estimator of the drifts by minimizing a ridge-regularized least-squares contrast over a B-spline basis. In particular, our theoretical findings reveal that the convergence rate of the resulting classifier is of order N -1/6+ε for any ε > 0, where N denotes the number of particles in each system. Numerical experiments illustrate the performance of the proposed method and show that it outperforms an end-to-end neural network baseline that does not exploit the underlying particle-system structure.
Related
- Trajectory-Planning Attitude Control System for Satellites with Magnetic Attitude Control and One Reaction Wheel
- Chapter 2: Geometry of the Fitness Surface and Trajectory Dynamics of Replicator Systems
- Trajectory-Initialized Neural Double Q-Routing for Large-Scale Overhead Hoist Transport Systems
- A Functional Central Limit Theorem For A Rank-Killed Particle System With Persistent Copies
- Derivation of the Enskog--Enskog System from a Particle System
BibTeX
@misc{denis2026drives,
title = {{Who Drives the System? Classifying Mean-Field Particle Systems from Trajectory Data}},
author = {Christophe Denis and Charlotte Dion-Blanc and Yating Liu},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35374},
eprint = {2609.35374},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05767719v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Who Drives the System? Classifying Mean-Field Particle Systems from Trajectory Data
AU - Christophe Denis
AU - Charlotte Dion-Blanc
AU - Yating Liu
PY - 2026
DA - 2026/09/28
PB - HAL
DO - 10.48550/arxiv.2609.35374
UR - https://hal.science/hal-05767719v2
AB - We study the supervised classification problem for interacting particle systems (IPS) from trajectory observations. The IPS belongs to one of K classes, each characterized by a distinct interaction drift. Given a learning dataset, the goal is then to predict the class label of a newly observed system based on the trajectory of a single particle. This setting raises several statistical challenges. First, the particles within each system interact and are therefore dependent. Second, although the full particle system is Markovian, the trajectory of a single particle is not. To address these difficulties, we exploit the McKean-Vlasov limit of the IPS, which describes the dynamics of a typical particle as the number of particles tends to infinity. We propose a plug-in classification procedure based on estimating the interaction drift associated with each class from discretely observed trajectory data. Hence, for each class, we provide a new nonparametric estimator of the drifts by minimizing a ridge-regularized least-squares contrast over a B-spline basis. In particular, our theoretical findings reveal that the convergence rate of the resulting classifier is of order N -1/6+ε for any ε > 0, where N denotes the number of particles in each system. Numerical experiments illustrate the performance of the proposed method and show that it outperforms an end-to-end neural network baseline that does not exploit the underlying particle-system structure.
ER -