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 · Thu Mar 11 00:00:00 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

References (30)

Fractional calculus in hydrologic modeling: A numerical perspective Benson, David A.; Meerschaert, Mark M.; Revielle, Jordan Advances in Water Resources, Vol. 51 https://doi.org/10.1016/j.advwatres.2012.04.005	journal	January 2013
Fractal mobile/immobile solute transport: FRACTAL MOBILE-IMMOBILE SOLUTE TRANSPORT Schumer, Rina; Benson, David A.; Meerschaert, Mark M. Water Resources Research, Vol. 39, Issue 10 https://doi.org/10.1029/2003wr002141	journal	October 2003
Parameter estimation for fractional transport: A particle-tracking approach: FRACTIONAL PARAMETER ESTIMATION Chakraborty, Paramita; Meerschaert, Mark M.; Lim, Chae Young Water Resources Research, Vol. 45, Issue 10 https://doi.org/10.1029/2008wr007577	journal	October 2009
Improving the accuracy of risk prediction from particle-based breakthrough curves reconstructed with kernel density estimators: IMPROVED ACCURACY RISK FROM KDE RECONSTRUCTED BTCS Siirila-Woodburn, Erica R.; Fernàndez-Garcia, Daniel; Sanchez-Vila, Xavier Water Resources Research, Vol. 51, Issue 6 https://doi.org/10.1002/2014WR016394	journal	June 2015
Lagrangian simulation of mixing and reactions in complex geochemical systems: COMPLEX REACTIONS ON PARTICLES Engdahl, Nicholas B.; Benson, David A.; Bolster, Diogo Water Resources Research, Vol. 53, Issue 4 https://doi.org/10.1002/2017WR020362	journal	April 2017
A KDE-Based Random Walk Method for Modeling Reactive Transport With Complex Kinetics in Porous Media: COMPLEX KINETIC REACTIONS IN RANDOM WALK Sole-Mari, Guillem; Fernàndez-Garcia, Daniel; Rodríguez-Escales, Paula Water Resources Research, Vol. 53, Issue 11 https://doi.org/10.1002/2017WR021064	journal	November 2017
Elimination of the Reaction Rate “Scale Effect”: Application of the Lagrangian Reactive Particle-Tracking Method to Simulate Mixing-Limited, Field-Scale Biodegradation at the Schoolcraft (MI, USA) Site: FIELD-SCALE REACTIVE PARTICLE TRACKING Ding, Dong; Benson, David A.; Fernàndez-Garcia, Daniel Water Resources Research, Vol. 53, Issue 12 https://doi.org/10.1002/2017WR021103	journal	December 2017
Pore‐Scale Hydrodynamics in a Progressively Bioclogged Three‐Dimensional Porous Medium: 3‐D Particle Tracking Experiments and Stochastic Transport Modeling Carrel, M.; Morales, V. L.; Dentz, M. Water Resources Research, Vol. 54, Issue 3 https://doi.org/10.1002/2017WR021726	journal	March 2018
Root n bandwidths selectors in multivariate kernel density estimation Wu, Tiee-Jian; Tsai, Min-Hsiao Probability Theory and Related Fields, Vol. 129, Issue 4 https://doi.org/10.1007/s00440-004-0357-8	journal	April 2004
Modeling bimolecular reactions and transport in porous media via particle tracking Ding, Dong; Benson, David A.; Paster, Amir Advances in Water Resources, Vol. 53 https://doi.org/10.1016/j.advwatres.2012.11.001	journal	March 2013
An automatic locally-adaptive method to estimate heavily-tailed breakthrough curves from particle distributions Pedretti, Daniele; Fernàndez-Garcia, Daniel Advances in Water Resources, Vol. 59 https://doi.org/10.1016/j.advwatres.2013.05.006	journal	September 2013
Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes Kang, Peter K.; Dentz, Marco; Le Borgne, Tanguy Advances in Water Resources, Vol. 106 https://doi.org/10.1016/j.advwatres.2017.03.024	journal	August 2017
On the separate treatment of mixing and spreading by the reactive-particle-tracking algorithm: An example of accurate upscaling of reactive Poiseuille flow Benson, David A.; Pankavich, Stephen; Bolster, Diogo Advances in Water Resources, Vol. 123 https://doi.org/10.1016/j.advwatres.2018.11.001	journal	January 2019
Numerical equivalence between SPH and probabilistic mass transfer methods for Lagrangian simulation of dispersion Sole-Mari, Guillem; Schmidt, Michael J.; Pankavich, Stephen D. Advances in Water Resources, Vol. 126 https://doi.org/10.1016/j.advwatres.2019.02.009	journal	April 2019
Entropy: (1) The former trouble with particle-tracking simulation, and (2) A measure of computational information penalty Benson, David A.; Pankavich, Stephen; Schmidt, Michael J. Advances in Water Resources, Vol. 137 https://doi.org/10.1016/j.advwatres.2020.103509	journal	March 2020
PAR 2 : Parallel Random Walk Particle Tracking Method for solute transport in porous media Rizzo, Calogero B.; Nakano, Aiichiro; de Barros, Felipe P. J. Computer Physics Communications, Vol. 239 https://doi.org/10.1016/j.cpc.2019.01.013	journal	June 2019
Optimal reconstruction of concentrations, gradients and reaction rates from particle distributions Fernàndez-Garcia, D.; Sanchez-Vila, X. Journal of Contaminant Hydrology, Vol. 120-121 https://doi.org/10.1016/j.jconhyd.2010.05.001	journal	March 2011
A Kernel-based Lagrangian method for imperfectly-mixed chemical reactions Schmidt, Michael J.; Pankavich, Stephen; Benson, David A. Journal of Computational Physics, Vol. 336 https://doi.org/10.1016/j.jcp.2017.02.012	journal	May 2017
A variable bandwidth selector in multivariate kernel density estimation Wu, Tiee-Jian; Chen, Ching-Fu; Chen, Huang-Yu Statistics & Probability Letters, Vol. 77, Issue 4 https://doi.org/10.1016/j.spl.2006.08.013	journal	February 2007
Fractal mobile/immobile solute transport: FRACTAL MOBILE-IMMOBILE SOLUTE TRANSPORT Schumer, Rina; Benson, David A.; Meerschaert, Mark M. Water Resources Research, Vol. 39, Issue 10 https://doi.org/10.1029/2003WR002141	journal	October 2003
Parameter estimation for fractional transport: A particle-tracking approach: FRACTIONAL PARAMETER ESTIMATION Chakraborty, Paramita; Meerschaert, Mark M.; Lim, Chae Young Water Resources Research, Vol. 45, Issue 10 https://doi.org/10.1029/2008WR007577	journal	October 2009
Upscaling of Mixing‐Limited Bimolecular Chemical Reactions in Poiseuille Flow Perez, Lazaro J.; Hidalgo, Juan J.; Dentz, Marco Water Resources Research, Vol. 55, Issue 1 https://doi.org/10.1029/2018WR022730	journal	January 2019
Lagrangian Modeling of Reactive Transport in Heterogeneous Porous Media With an Automatic Locally Adaptive Particle Support Volume Sole‐Mari, Guillem; Fernàndez‐Garcia, Daniel Water Resources Research, Vol. 54, Issue 10 https://doi.org/10.1029/2018WR023033	journal	October 2018
Accelerating and Parallelizing Lagrangian Simulations of Mixing‐Limited Reactive Transport Engdahl, Nicholas B.; Schmidt, Michael J.; Benson, David A. Water Resources Research, Vol. 55, Issue 4 https://doi.org/10.1029/2018WR024361	journal	April 2019
Accelerated Multilevel Monte Carlo With Kernel‐Based Smoothing and Latinized Stratification Taverniers, Søren; Bosma, Sebastian B. M.; Tartakovsky, Daniel M. Water Resources Research, Vol. 56, Issue 9 https://doi.org/10.1029/2019WR026984	journal	August 2020
Random-Walk Simulation of Transport in Heterogeneous Porous Media: Local Mass-Conservation Problem and Implementation Methods LaBolle, Eric M.; Fogg, Graham E.; Tompson, Andrew F. B. Water Resources Research, Vol. 32, Issue 3 https://doi.org/10.1029/95WR03528	journal	March 1996
An iterative bandwidth selector for kernel estimation of densities and their derivatives Engel, Joachim; Herrmann, Eva; Gasser, Theo Journal of Nonparametric Statistics, Vol. 4, Issue 1 https://doi.org/10.1080/10485259408832598	journal	January 1994
A new look at the statistical model identification Akaike, H. IEEE Transactions on Automatic Control, Vol. 19, Issue 6 https://doi.org/10.1109/TAC.1974.1100705	journal	December 1974
On Bandwidth Variation in Kernel Estimates-A Square Root Law Abramson, Ian S. The Annals of Statistics, Vol. 10, Issue 4 https://doi.org/10.1214/aos/1176345986	journal	December 1982
Bandwidth Selection for Kernel Density Estimation Chiu, Shean-Tsong The Annals of Statistics, Vol. 19, Issue 4 https://doi.org/10.1214/aos/1176348376	journal	December 1991

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