Learning Interaction Kernels from Collective Steady States
Abstract
We propose a learning procedure for system identification in interacting particle systems from single-snapshot observations of collective behaviors, unlike existing approaches that rely on observations of trajectories. This setting leads to a fundamentally ill-posed inverse problem, which we solve by using a regularization strategy based on the empirical distribution of observed configurations, drawn from different, unobserved initial conditions. We test our learning procedure on a variety of representative models with steady-state and quasi-stationary patterns, where collective behaviors encode implicit information about the interaction mechanisms, demonstrating that our approach enables stable and accurate recovery of the underlying interaction laws, leading to faithful reproduction of the collective behavior, and in many cases even of the dynamics leading up to it.
Related
- Generalized Determinantal Point Processes for Attraction and Repulsion with Distinct Interaction Kernels
- Uniform-in-time propagation of chaos for singular Lk interaction kernels with rates
- A McLennan formula for equiaccessible steady states
- Ill-Posedness of the Euler Equations Linearized around Homogeneous Steady States
- Boltzmann-like occupation of nonequilibrium steady states on dense disordered networks
BibTeX
@misc{hao2026learning,
title = {{Learning Interaction Kernels from Collective Steady States}},
author = {Baoli Hao and Mauro Maggioni and Ming Zhong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12004},
eprint = {2609.12004},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12004},
}
RIS
TY - UNPB
TI - Learning Interaction Kernels from Collective Steady States
AU - Baoli Hao
AU - Mauro Maggioni
AU - Ming Zhong
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.12004
UR - https://arxiv.org/abs/2609.12004
AB - We propose a learning procedure for system identification in interacting particle systems from single-snapshot observations of collective behaviors, unlike existing approaches that rely on observations of trajectories. This setting leads to a fundamentally ill-posed inverse problem, which we solve by using a regularization strategy based on the empirical distribution of observed configurations, drawn from different, unobserved initial conditions. We test our learning procedure on a variety of representative models with steady-state and quasi-stationary patterns, where collective behaviors encode implicit information about the interaction mechanisms, demonstrating that our approach enables stable and accurate recovery of the underlying interaction laws, leading to faithful reproduction of the collective behavior, and in many cases even of the dynamics leading up to it.
ER -