论文标题
非参数，基于数据的内核插值，用于粒子跟踪模拟和内核密度估计
Nonparametric, data-based kernel interpolation for particle-tracking simulations and kernel density estimation
论文作者
论文摘要
用于粒子跟踪的传统插值技术包括使用预定的（即封闭形式，参数）内核的融合和卷积公式。在许多情况下，将粒子作为时间和空间中的点源引入，因此粒子的云（在时空或时间上）是基础PDE绿色功能的离散表示。因此，每个粒子都是绿色功能的样本。因此，每个粒子应根据绿色的功能分配。简而言之，粒子样品“云”的卷积插值的内核应为云本身的复制品。这个想法引起了一种迭代方法，在该方法中可以在插值绿色功能的过程中辨别内核的形式。当绿色的函数是密度时，此方法广泛适用于基于从单个分布中绘制的随机数据插值内核密度估计。我们制定和构建算法，并证明其对偏斜和/或重尾数据（包括突破曲线）进行核密度估计的能力。
Traditional interpolation techniques for particle tracking include binning and convolutional formulas that use pre-determined (i.e., closed-form, parameteric) kernels. In many instances, the particles are introduced as point sources in time and space, so the cloud of particles (either in space or time) is a discrete representation of the Green's function of an underlying PDE. As such, each particle is a sample from the Green's function; therefore, each particle should be distributed according to the Green's function. In short, the kernel of a convolutional interpolation of the particle sample "cloud" should be a replica of the cloud itself. This idea gives rise to an iterative method by which the form of the kernel may be discerned in the process of interpolating the Green's function. When the Green's function is a density, this method is broadly applicable to interpolating a kernel density estimate based on random data drawn from a single distribution. We formulate and construct the algorithm and demonstrate its ability to perform kernel density estimation of skewed and/or heavy-tailed data including breakthrough curves.
