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dc.contributor.advisorPankavich, Stephen
dc.contributor.advisorBenson, David A.
dc.contributor.authorTran, Nhat Thanh Van
dc.contributor.committeememberLeiderman, Karin
dc.contributor.committeememberTenorio, Luis
dc.date.accessioned2020-06-07T10:13:29Z
dc.date.available2020-06-07T10:13:29Z
dc.date.submitted2020
dc.descriptionIncludes bibliographical references.
dc.description2020 Spring
dc.description.abstractTraditional probabilistic methods for the estimation of parameters within advection-diffusion equations (ADEs) often overlook the entropic contribution of the discretization, i.e.number of particles, within associated numerical methods. Many times, the gain in accuracyof a highly discretized numerical model is outweighed by its associated computational costs.The research project herein seeks to answer the question of how many particles one should usein a numerical simulation to best approximate and estimate parameters in one-dimensionaladvective-diffusive transport with constant coefficients. To answer this question, we use thewell-known Akaike Information Criteria (AIC) and a recently-developed correction calledthe Computational Information Criteria (COMIC) to guide the model selection process.Two Lagrangian numerical methods - the random-walk particle tracking (RWPT) and mass-transfer particle tracking (MTPT) methods - are employed to solve the ADE at variouslevels of discretization. The numerical results demonstrate that the newly developed COMICprovides an optimal number of particles that can describe a more efficient model in termsof parameter estimation and model prediction compared to the model selected by the AIC.These results demonstrate the need for future modelers and scientific researchers to utilizecomputationally-driven selection criteria in order to best select numerical models.
dc.format.mediumborn digital
dc.format.mediummasters theses
dc.identifierTran_mines_0052N_11960.pdf
dc.identifierT 8938
dc.identifier.urihttps://hdl.handle.net/11124/174130
dc.languageEnglish
dc.publisherColorado School of Mines. Arthur Lakes Library
dc.relation.ispartof2020 - Mines Theses & Dissertations
dc.rightsCopyright of the original work is retained by the author.
dc.subjectcomputational criteria
dc.subjectparticles methods
dc.subjectentropy
dc.subjectCOMIC
dc.titleEntropic criteria for computational models of advection-diffusion equations
dc.typeText
thesis.degree.disciplineApplied Mathematics and Statistics
thesis.degree.grantorColorado School of Mines
thesis.degree.levelMasters
thesis.degree.nameMaster of Science (M.S.)


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