A Computational Information Criterion for Particle-Tracking with Sparse or Noisy Data

Tran, Nhat V.; Benson, David A.; Schmidt, Michael J.; Pankavich, Stephen D.

doi:10.1016/j.advwatres.2021.103893

A Computational Information Criterion for Particle-Tracking with Sparse or Noisy Data

Journal Article · Thu Mar 18 00:00:00 EDT 2021 · Advances in Water Resources

DOI:https://doi.org/10.1016/j.advwatres.2021.103893· OSTI ID:1778026

Tran, Nhat V. ^[1]; Benson, David A. ^[2]; Schmidt, Michael J. ^[3]; Pankavich, Stephen D. ^[2]

Univ. of California, Irvine, CA (United States)
Colorado School of Mines, Golden, CO (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research

Traditional probabilistic methods for the simulation of advection-diffusion equations (ADEs) often overlook the entropic contribution of the discretization, e.g., the number of particles, within associated numerical methods. Many times, the gain in accuracy of a highly discretized numerical model is outweighed by its associated computational costs or the noise within the data. Herein, we address the question of how many particles are needed in a simulation to best approximate and estimate parameters in one-dimensional advective-diffusive transport. To do so, we use the well-known Akaike Information Criterion (AIC) and a recently-developed correction called the Computational Information Criterion (COMIC) to guide the model selection process. Random-walk and mass-transfer particle tracking methods are employed to solve the model equations at various levels of discretization. Numerical results demonstrate that the COMIC provides an optimal number of particles that can describe a more efficient model in terms of parameter estimation and model prediction compared to the model selected by the AIC even when the data is sparse or noisy, the sampling volume is not uniform throughout the physical domain, or the error distribution of the data is non-IID Gaussian.

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; NA0003525

OSTI ID:: 1778026

Report Number(s):: SAND--2021-3538J; 695040

Journal Information:: Advances in Water Resources, Journal Name: Advances in Water Resources Vol. 151; ISSN 0309-1708

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (19)

Arbitrarily complex chemical reactions on particles: REACTIVE PARTICLE TRACKING Benson, David A.; Bolster, Diogo Water Resources Research, Vol. 52, Issue 11 https://doi.org/10.1002/2016WR019368	journal	November 2016
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
The future of distributed models: Model calibration and uncertainty prediction Beven, Keith; Binley, Andrew Hydrological Processes, Vol. 6, Issue 3 https://doi.org/10.1002/hyp.3360060305	journal	July 1992
Unifying the derivations for the Akaike and corrected Akaike information criteria Cavanaugh, Joseph E. Statistics & Probability Letters, Vol. 33, Issue 2 https://doi.org/10.1016/S0167-7152(96)00128-9	journal	April 1997
A meshless method to simulate solute transport in heterogeneous porous media Herrera, Paulo A.; Massabó, Marco; Beckie, Roger D. Advances in Water Resources, Vol. 32, Issue 3 https://doi.org/10.1016/j.advwatres.2008.12.005	journal	March 2009
On the accuracy of simulating mixing by random-walk particle-based mass-transfer algorithms Schmidt, Michael J.; Pankavich, Stephen D.; Benson, David A. Advances in Water Resources, Vol. 117 https://doi.org/10.1016/j.advwatres.2018.05.003	journal	July 2018
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
A mass-transfer particle-tracking method for simulating transport with discontinuous diffusion coefficients Schmidt, Michael J.; Engdahl, Nicholas B.; Pankavich, Stephen D. Advances in Water Resources, Vol. 140 https://doi.org/10.1016/j.advwatres.2020.103577	journal	June 2020
A review and numerical assessment of the random walk particle tracking method Salamon, Peter; Fernàndez-Garcia, Daniel; Gómez-Hernández, J. Jaime Journal of Contaminant Hydrology, Vol. 87, Issue 3-4 https://doi.org/10.1016/j.jconhyd.2006.05.005	journal	October 2006
Maximum likelihood Bayesian averaging of spatial variability models in unsaturated fractured tuff: MAXIMUM LIKELIHOOD BAYESIAN MODEL AVERAGING Ye, Ming; Neuman, Shlomo P.; Meyer, Philip D. Water Resources Research, Vol. 40, Issue 5 https://doi.org/10.1029/2003WR002557	journal	May 2004
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
Lagrangian Modeling of Mixing‐Limited Reactive Transport in Porous Media: Multirate Interaction by Exchange With the Mean Sole‐Mari, Guillem; Fernàndez‐Garcia, Daniel; Sanchez‐Vila, Xavier Water Resources Research, Vol. 56, Issue 8 https://doi.org/10.1029/2019WR026993	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
Regression and time series model selection in small samples Hurvich, Clifford M.; Tsai, Chih-Ling Biometrika, Vol. 76, Issue 2 https://doi.org/10.1093/biomet/76.2.297	journal	January 1989
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
Multimodel Ranking and Inference in Ground Water Modeling Poeter, Eileen; Anderson, David Ground Water, Vol. 43, Issue 4 https://doi.org/10.1111/j.1745-6584.2005.0061.x	journal	July 2005
On Information and Sufficiency Kullback, S.; Leibler, R. A. The Annals of Mathematical Statistics, Vol. 22, Issue 1 https://doi.org/10.1214/aoms/1177729694	journal	March 1951

Similar Records

An approach with the Akaike information criterion to the radiation distribution reconstruction of toroidal plasma

Journal Article · Thu Oct 01 00:00:00 EDT 1987 · IEEE Trans. Plasma Sci.; (United States) · OSTI ID:5454644

Choosing the optimal fit function: Comparison of the Akaike information criterion and the F-test

Journal Article · Wed Nov 14 23:00:00 EST 2007 · Medical Physics · OSTI ID:21032840

Related Subjects

97 MATHEMATICS AND COMPUTING
Computational information criterion
Lagrangian modeling
diffusion-reaction equation
non-Gaussian error distribution
particle methods

A Computational Information Criterion for Particle-Tracking with Sparse or Noisy Data

Citation Formats

References (19)

Similar Records

Related Subjects