Nonparametric, data-based kernel interpolation for particle-tracking simulations and kernel density estimation

Benson, David A.; Bolster, Diogo; Pankavich, Stephen; Schmidt, Michael John

doi:10.1016/j.advwatres.2021.103889

Nonparametric, data-based kernel interpolation for particle-tracking simulations and kernel density estimation

Journal Article · Wed Mar 10 23:00:00 EST 2021 · Advances in Water Resources

DOI:https://doi.org/10.1016/j.advwatres.2021.103889· OSTI ID:1778025

Benson, David A. ^[1]; Bolster, Diogo ^[2]; Pankavich, Stephen ^[1]; Schmidt, Michael John ^[3]

Colorado School of Mines, Golden, CO (United States)
Univ. of Notre Dame, IN (United States)
Sandia National Lab. (SNL-CA), Livermore, CA (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1778025

Report Number(s):: SAND--2021-3537J; 695039

Journal Information:: Advances in Water Resources, Journal Name: Advances in Water Resources Vol. 152; ISSN 0309-1708

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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