论文标题
从基于代理系统的观察结果中学习交互变量和内核
Learning Interaction Variables and Kernels from Observations of Agent-Based Systems
论文作者
论文摘要
许多学科的动态系统被建模为相互作用的粒子或试剂，其相互作用规则取决于非常少量的变量（例如，成对距离，相位的成对差异等...），这是代理对状态的函数。然而，这些相互作用规则可以产生自组织的动力学，并具有复杂的紧急行为（聚类，羊群，蜂群等）。我们提出了一种学习技术，鉴于对沿着代理的轨迹的状态和速度的观察，它以非参数方式产生了相互作用内核所依赖的变量和相互作用内核本身。这产生了有效的维度降低，从而避免了高维观测数据（所有试剂的状态和速度）的维度诅咒。我们证明了我们方法对各种一阶交互系统的学习能力。
Dynamical systems across many disciplines are modeled as interacting particles or agents, with interaction rules that depend on a very small number of variables (e.g. pairwise distances, pairwise differences of phases, etc...), functions of the state of pairs of agents. Yet, these interaction rules can generate self-organized dynamics, with complex emergent behaviors (clustering, flocking, swarming, etc.). We propose a learning technique that, given observations of states and velocities along trajectories of the agents, yields both the variables upon which the interaction kernel depends and the interaction kernel itself, in a nonparametric fashion. This yields an effective dimension reduction which avoids the curse of dimensionality from the high-dimensional observation data (states and velocities of all the agents). We demonstrate the learning capability of our method to a variety of first-order interacting systems.
