从集体稳态中学习交互核
Learning Interaction Kernels from Collective Steady States
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中文总结 AI 辅助
本文提出一种基于单快照集体观测的正则化学习方法，用于从稳态中稳定恢复相互作用粒子系统的交互核，并准确再现集体行为及动力学。
中文摘要 AI 辅助
我们提出了一种用于相互作用粒子系统中系统辨识的学习程序，该程序基于集体行为的单快照观测，不同于依赖轨迹观测的现有方法。这一设定导致了一个本质上不适定的逆问题，我们通过使用基于观测构型经验分布的正则化策略来解决该问题，这些构型来自不同的、未观测的初始条件。我们在多种具有稳态和准稳态模式的代表性模型上测试了我们的学习程序，在这些模型中，集体行为编码了关于交互机制的隐式信息，证明了我们的方法能够稳定且准确地恢复潜在的交互规律，从而忠实再现集体行为，并且在许多情况下甚至能再现导致该行为的动力学过程。
英文摘要
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.
发表机构
- Illinois Institute of Technology（伊利诺伊理工学院）
- Johns Hopkins University（约翰斯·霍普金斯大学）
- University of Houston（休斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。
