{"id":{"repo_id":"colo-mines","oai_identifier":"oai:repository.mines.edu:11124/174130"},"canonical_url":"https://search.dev.ndltd.org/etd/colo-mines/oai:repository.mines.edu:11124/174130","repository":{"repo_id":"colo-mines","name":"Colorado School of Mines","base_url":"https://repository.mines.edu/server/oai/request"},"display":{"title":"Entropic criteria for computational models of advection-diffusion equations","abstract":"Traditional 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.","abstract_html":"Traditional 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.","abstract_has_math":false,"creators":["Tran, Nhat Thanh Van"],"institution":"Colorado School of Mines. Arthur Lakes Library","degree_name":"Master of Science (M.S.)","degree_level":"Masters","degree_discipline":"Applied Mathematics and Statistics","degree_department":null,"school":null,"contributors":[],"advisors":["Pankavich, Stephen","Benson, David A."],"committee_chairs":[],"committee_members":["Leiderman, Karin","Tenorio, Luis"],"year":2020,"date_issued":"2020","date_published":"2020","updated_at":"2026-07-24T01:43:42Z","subjects":["computational criteria","particles methods","entropy","COMIC"],"languages":["eng","English"],"rights":["Copyright of the original work is retained by the author."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["T 8938"],"render_values":[{"text":"T 8938","href":null,"code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/11124/174130","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Pankavich, Stephen","Benson, David A."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Leiderman, Karin","Tenorio, Luis"]},{"key":"dc:creator","label":"Author","values":["Tran, Nhat Thanh Van"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-06-07T10:13:29Z","2022-02-03T13:19:09Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-06-07T10:13:29Z","2022-02-03T13:19:09Z"]},{"key":"dc:date.issued","label":"Date","values":["2020"]},{"key":"dc:publisher","label":"Institution","values":["Colorado School of Mines. Arthur Lakes Library"]},{"key":"dc:type","label":"Dc Type","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Applied Mathematics and Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (M.S.)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Colorado School of Mines"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["computational criteria","particles methods","entropy","COMIC"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright of the original work is retained by the author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["Tran_mines_0052N_11960.pdf","T 8938"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/11124/174130"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Includes bibliographical references.","2020 Spring."]},{"key":"dc:description.abstract","label":"Abstract","values":["Traditional 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."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["born digital","masters theses"]},{"key":"dc:title","label":"Title","values":["Entropic criteria for computational models of advection-diffusion equations"]}]}],"canonical_facts":{"dc:contributor.advisor":["Pankavich, Stephen","Benson, David A."],"dc:contributor.committeemember":["Leiderman, Karin","Tenorio, Luis"],"dc:creator":["Tran, Nhat Thanh Van"],"dc:date.accessioned":["2020-06-07T10:13:29Z","2022-02-03T13:19:09Z"],"dc:date.available":["2020-06-07T10:13:29Z","2022-02-03T13:19:09Z"],"dc:date.issued":["2020"],"dc:description":["Includes bibliographical references.","2020 Spring."],"dc:description.abstract":["Traditional 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.medium":["born digital","masters theses"],"dc:identifier":["Tran_mines_0052N_11960.pdf","T 8938"],"dc:identifier.uri":["https://hdl.handle.net/11124/174130"],"dc:language":["English"],"dc:language.iso":["eng"],"dc:publisher":["Colorado School of Mines. Arthur Lakes Library"],"dc:rights":["Copyright of the original work is retained by the author."],"dc:subject":["computational criteria","particles methods","entropy","COMIC"],"dc:title":["Entropic criteria for computational models of advection-diffusion equations"],"dc:type":["Text"],"thesis:degree_discipline":["Applied Mathematics and Statistics"],"thesis:degree_level":["Masters"],"thesis:degree_name":["Master of Science (M.S.)"],"thesis:institution_name":["Colorado School of Mines"]},"updated_at":"2026-07-24T01:43:42Z"}