{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/76101"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/76101","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"A learning method for the approximation of discontinuous functions for stochastic simulations","abstract":"Surrogate models for computational simulations are inexpensive input-output approximations that allow expensive analyses, such as the forward propagation of uncertainty and Bayesian statistical inference, to be performed efficiently. When a simulation output does not depend smoothly on its inputs, however, most existing surrogate construction methodologies yield large errors and slow convergence rates. This thesis develops a new methodology for approximating simulation outputs that depend discontinuously on input parameters. Our approach focuses on piecewise smooth outputs and involves two stages: first, efficient detection and localization of discontinuities in high-dimensional parameter spaces using polynomial annihilation, support vector machine classification, and uncertainty sampling; second, approximation of the output on each region using Gaussian process regression. The discontinuity detection methodology is illustrated on examples of up to 11 dimensions, including algebraic models and ODE systems, demonstrating improved scaling and efficiency over other methods found in the literature. Finally, the complete surrogate construction approach is demonstrated on two physical models exhibiting canonical discontinuities: shock formation in Burgers' equation and autoignition in hydrogen-oxygen combustion.","abstract_html":"Surrogate models for computational simulations are inexpensive input-output approximations that allow expensive analyses, such as the forward propagation of uncertainty and Bayesian statistical inference, to be performed efficiently. When a simulation output does not depend smoothly on its inputs, however, most existing surrogate construction methodologies yield large errors and slow convergence rates. This thesis develops a new methodology for approximating simulation outputs that depend discontinuously on input parameters. Our approach focuses on piecewise smooth outputs and involves two stages: first, efficient detection and localization of discontinuities in high-dimensional parameter spaces using polynomial annihilation, support vector machine classification, and uncertainty sampling; second, approximation of the output on each region using Gaussian process regression. The discontinuity detection methodology is illustrated on examples of up to 11 dimensions, including algebraic models and ODE systems, demonstrating improved scaling and efficiency over other methods found in the literature. Finally, the complete surrogate construction approach is demonstrated on two physical models exhibiting canonical discontinuities: shock formation in Burgers' equation and autoignition in hydrogen-oxygen combustion.","abstract_has_math":false,"creators":["Gorodetsky, Alex Arkady"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.","school":null,"contributors":[],"advisors":["Youssef Marzouk."],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012","date_published":"2012","updated_at":"2026-07-22T22:20:59Z","subjects":["Aeronautics and Astronautics."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/76101","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Youssef Marzouk."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics."]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. 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When a simulation output does not depend smoothly on its inputs, however, most existing surrogate construction methodologies yield large errors and slow convergence rates. This thesis develops a new methodology for approximating simulation outputs that depend discontinuously on input parameters. Our approach focuses on piecewise smooth outputs and involves two stages: first, efficient detection and localization of discontinuities in high-dimensional parameter spaces using polynomial annihilation, support vector machine classification, and uncertainty sampling; second, approximation of the output on each region using Gaussian process regression. The discontinuity detection methodology is illustrated on examples of up to 11 dimensions, including algebraic models and ODE systems, demonstrating improved scaling and efficiency over other methods found in the literature. Finally, the complete surrogate construction approach is demonstrated on two physical models exhibiting canonical discontinuities: shock formation in Burgers' equation and autoignition in hydrogen-oxygen combustion."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:title","label":"Title","values":["A learning method for the approximation of discontinuous functions for stochastic simulations"]}]}],"canonical_facts":{"dc:contributor.advisor":["Youssef Marzouk."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics."],"dc:contributor.other":["Massachusetts Institute of Technology. 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Our approach focuses on piecewise smooth outputs and involves two stages: first, efficient detection and localization of discontinuities in high-dimensional parameter spaces using polynomial annihilation, support vector machine classification, and uncertainty sampling; second, approximation of the output on each region using Gaussian process regression. The discontinuity detection methodology is illustrated on examples of up to 11 dimensions, including algebraic models and ODE systems, demonstrating improved scaling and efficiency over other methods found in the literature. 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