Learning Interaction Kernels from Collective Steady States

2026-09-09

AI Summary

本文提出一种从单次观测集体行为识别粒子系统交互核的学习方法，通过基于观测配置的经验分布的正则化策略解决病态逆问题。

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.

Problem

• interacting particle systems
• single-snapshot observations
• ill-posed inverse problem
• collective behaviors

Innovation

• single-snapshot observations
• regularization strategy
• empirical distribution
• interaction laws
• collective behavior