Discovery of interaction and diffusion kernels in particle-to-mean-field multi-agent systems

2026-03-16

AI Summary

针对多智能体系统中交互与扩散核未知的问题，提出基于轨迹数据的稀疏回归方法，结合随机批采样与平均场近似进行有效识别。

Technology Category

• Multiagent Systems: Multiagent Learning
• Machine Learning: Multi-instance/Multi-view Learning
• Intelligent Robots: Multi-Robot Systems

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

We propose a data-driven framework to learn interaction kernels in stochastic multi-agent systems. Our approach aims at identifying the functional form of nonlocal interaction and diffusion terms directly from trajectory data, without any a priori knowledge of the underlying interaction structure. Starting from a discrete stochastic binary-interaction model, we formulate the inverse problem as a sequence of sparse regression tasks in structured finite-dimensional spaces spanned by compactly supported basis functions, such as piecewise linear polynomials. In particular, we assume that pairwise interactions between agents are not directly observed and that only limited trajectory data are available. To address these challenges, we propose two complementary identification strategies. The first based on random-batch sampling, which compensates for latent interactions while preserving the statistical structure of the full dynamics in expectation. The second based on a mean-field approximation, where the empirical particle density reconstructed from the data defines a continuous nonlocal regression problem. Numerical experiments demonstrate the effectiveness and robustness of the proposed framework, showing accurate reconstruction of both interaction and diffusion kernels even from partially observed. The method is validated on benchmark models, including bounded-confidence and attraction-repulsion dynamics, where the two proposed strategies achieve comparable levels of accuracy.

Problem

• multi-agent systems
• interaction kernels
• diffusion kernels
• inverse problem
• trajectory data

Innovation

• data-driven learning
• interaction kernels
• diffusion kernels
• sparse regression
• mean-field approximation