论文标题
从单个标题数据中相互作用粒子系统中势能的最大似然估计
Maximum likelihood estimation of potential energy in interacting particle systems from single-trajectory data
论文作者
论文摘要
本文涉及从连续时间和单个对象数据相互作用的粒子系统中二次势能的参数估计问题。即使这种动力学系统是高维系统，我们也表明，香草最大似然估计器（无正则化）能够在平均场限制和长时间动力学中同时同时估算相互作用的电势参数。在某些方面，这避免了对粒子相互作用对称性下的大型动态系统的诅咒。
This paper concerns the parameter estimation problem for the quadratic potential energy in interacting particle systems from continuous-time and single-trajectory data. Even though such dynamical systems are high-dimensional, we show that the vanilla maximum likelihood estimator (without regularization) is able to estimate the interaction potential parameter with optimal rate of convergence simultaneously in mean-field limit and in long-time dynamics. This to some extend avoids the curse-of-dimensionality for estimating large dynamical systems under symmetry of the particle interaction.
