{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/31542"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/31542","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"On the Effect of Numerical Noise in Simulation-Based Optimization","abstract":"Numerical noise is a prevalent concern in many practical optimization problems. Convergence of gradient based optimization algorithms in the presence of numerical noise is not always assured. One way to improve optimization algorithm performance in the presence of numerical noise is to adjust the method of gradient computation. This study investigates the use of Continuous Sensitivity Equation (CSE) gradient approximations in the context of numerical noise and optimization. Three problems are considered: a problem with a system of ODE constraints, a single parameter flow problem constrained by the Navier-Stokes equations, and a multiple parameter flow problem constrained by the Navier-Stokes equations. All three problems use adaptive methods in the simulation of the constraint and are numerically noisy. Gradients for each problem are computed with both CSE and finite difference methods. The gradients are analyzed and compared. The two flow problems are optimized with a trust region optimization algorithm using both sets of gradient calculations. Optimization results are also compared, and the CSE gradient approximation yields impressive results for these examples.","abstract_html":"Numerical noise is a prevalent concern in many practical optimization problems. Convergence of gradient based optimization algorithms in the presence of numerical noise is not always assured. One way to improve optimization algorithm performance in the presence of numerical noise is to adjust the method of gradient computation. This study investigates the use of Continuous Sensitivity Equation (CSE) gradient approximations in the context of numerical noise and optimization. Three problems are considered: a problem with a system of ODE constraints, a single parameter flow problem constrained by the Navier-Stokes equations, and a multiple parameter flow problem constrained by the Navier-Stokes equations. All three problems use adaptive methods in the simulation of the constraint and are numerically noisy. Gradients for each problem are computed with both CSE and finite difference methods. The gradients are analyzed and compared. The two flow problems are optimized with a trust region optimization algorithm using both sets of gradient calculations. Optimization results are also compared, and the CSE gradient approximation yields impressive results for these examples.","abstract_has_math":false,"creators":["Vugrin, Kay E."],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Borggaard, Jeffrey T."],"committee_members":["Cliff, Eugene M.","Sun, Shu-Ming","Herdman, Terry L."],"year":2003,"date_issued":"2003-03-12","date_published":"2003-03-12","updated_at":"2026-07-22T22:18:50Z","subjects":["trust region algorithm","sensitivity analysis","shape optimization"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-03252003-213320"],"render_values":[{"text":"etd-03252003-213320","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/31542","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Borggaard, Jeffrey T."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Cliff, Eugene M.","Sun, Shu-Ming","Herdman, Terry L."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Vugrin, Kay E."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:32:51Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:32:51Z","2004-04-10"]},{"key":"dc:date.issued","label":"Date","values":["2003-03-12"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["trust region algorithm","sensitivity analysis","shape optimization"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-03252003-213320"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/31542"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Numerical noise is a prevalent concern in many practical optimization problems. Convergence of gradient based optimization algorithms in the presence of numerical noise is not always assured. One way to improve optimization algorithm performance in the presence of numerical noise is to adjust the method of gradient computation. This study investigates the use of Continuous Sensitivity Equation (CSE) gradient approximations in the context of numerical noise and optimization. Three problems are considered: a problem with a system of ODE constraints, a single parameter flow problem constrained by the Navier-Stokes equations, and a multiple parameter flow problem constrained by the Navier-Stokes equations. All three problems use adaptive methods in the simulation of the constraint and are numerically noisy. Gradients for each problem are computed with both CSE and finite difference methods. The gradients are analyzed and compared. The two flow problems are optimized with a trust region optimization algorithm using both sets of gradient calculations. Optimization results are also compared, and the CSE gradient approximation yields impressive results for these examples."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["On the Effect of Numerical Noise in Simulation-Based Optimization"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Borggaard, Jeffrey T."],"dc:contributor.committeemember":["Cliff, Eugene M.","Sun, Shu-Ming","Herdman, Terry L."],"dc:contributor.department":["Mathematics"],"dc:creator":["Vugrin, Kay E."],"dc:date.accessioned":["2014-03-14T20:32:51Z"],"dc:date.available":["2014-03-14T20:32:51Z","2004-04-10"],"dc:date.issued":["2003-03-12"],"dc:description.abstract":["Numerical noise is a prevalent concern in many practical optimization problems. Convergence of gradient based optimization algorithms in the presence of numerical noise is not always assured. One way to improve optimization algorithm performance in the presence of numerical noise is to adjust the method of gradient computation. This study investigates the use of Continuous Sensitivity Equation (CSE) gradient approximations in the context of numerical noise and optimization. Three problems are considered: a problem with a system of ODE constraints, a single parameter flow problem constrained by the Navier-Stokes equations, and a multiple parameter flow problem constrained by the Navier-Stokes equations. All three problems use adaptive methods in the simulation of the constraint and are numerically noisy. Gradients for each problem are computed with both CSE and finite difference methods. The gradients are analyzed and compared. The two flow problems are optimized with a trust region optimization algorithm using both sets of gradient calculations. 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