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This research introduces a novel machine learning framework for system identification in interacting particle systems, enabling the recovery of interaction laws from single-snapshot observations rather than full trajectory data. By leveraging regularization based on empirical distributions, the method addresses an ill-posed inverse problem to accurately reconstruct underlying dynamics and steady-state patterns. This advancement is significant for analyzing complex collective behaviors where traditional temporal data collection is impractical.
Learning Interaction Kernels from Collective Steady States
arXiv:2609.12004v1 Announce Type: cross 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.
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.
Machine Learning (stat.ML); Machine Learning (cs.LG); Dynamical Systems (math.DS); Numerical Analysis (math.NA); Adaptation and Self-Organizing Systems (nlin.AO)
arXiv:2609.12004 [stat.ML]
(or arXiv:2609.12004v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2609.12004 arXiv-issued DOI via DataCite (pending registration)
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