{"id":{"repo_id":"calgary","oai_identifier":"oai:ucalgary.scholaris.ca:1880/112515"},"canonical_url":"https://search.dev.ndltd.org/etd/calgary/oai:ucalgary.scholaris.ca:1880/112515","repository":{"repo_id":"calgary","name":"University of Calgary","base_url":"https://ucalgary.scholaris.ca/server/oai/request"},"display":{"title":"Numerical approximations of coupled forward-backward SPDEs with applications","abstract":"We introduce a new scheme combining the finite element method and machine learning techniques for the numerical approximations of coupled forward-backward stochastic partial differential equations (FBSPDEs) with homogeneous Dirichlet boundary conditions. For the FBSPDE, the finite element method in the spatial domain leads to approximations by finite-dimensional forward-backward stochastic differential equations (FBSDEs) in the temporal domain. We then approximate the solution of FBSDE by some existing machine learning schemes. Strong convergence results for spatial discretization of FBSPDEs are addressed.","abstract_html":"We introduce a new scheme combining the finite element method and machine learning techniques for the numerical approximations of coupled forward-backward stochastic partial differential equations (FBSPDEs) with homogeneous Dirichlet boundary conditions. For the FBSPDE, the finite element method in the spatial domain leads to approximations by finite-dimensional forward-backward stochastic differential equations (FBSDEs) in the temporal domain. We then approximate the solution of FBSDE by some existing machine learning schemes. Strong convergence results for spatial discretization of FBSPDEs are addressed.","abstract_has_math":false,"creators":["Molla, Md Hasib Uddin"],"institution":"Science","degree_name":"Master of Science (MSc)","degree_level":null,"degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":[],"advisors":["Qiu, Jinniao"],"committee_chairs":[],"committee_members":["Ware, Antony Frank","Swishchuk, Anatoliy V."],"year":2020,"date_issued":"2020-09-10","date_published":"2020-09-10","updated_at":"2026-07-24T01:30:13Z","subjects":["Stochastic partial differential equations","deep learning"],"languages":["eng"],"rights":["University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["http://dx.doi.org/10.11575/PRISM/38185"],"render_values":[{"text":"http://dx.doi.org/10.11575/PRISM/38185","href":"http://dx.doi.org/10.11575/PRISM/38185","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/1880/112515","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Qiu, Jinniao"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Ware, Antony Frank","Swishchuk, Anatoliy V."]},{"key":"dc:creator","label":"Author","values":["Molla, Md Hasib Uddin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020-11"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-09-11T22:31:22Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-09-11T22:31:22Z"]},{"key":"dc:date.issued","label":"Date","values":["2020-09-10"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Calgary"]},{"key":"dc:type","label":"Dc Type","values":["master thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics & Statistics"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MSc)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Calgary"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Stochastic partial differential equations","deep learning"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["University of Calgary graduate students retain copyright ownership and moral rights for their thesis. 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For the FBSPDE, the finite element method in the spatial domain leads to approximations by finite-dimensional forward-backward stochastic differential equations (FBSDEs) in the temporal domain. We then approximate the solution of FBSDE by some existing machine learning schemes. Strong convergence results for spatial discretization of FBSPDEs are addressed."]},{"key":"dc:title","label":"Title","values":["Numerical approximations of coupled forward-backward SPDEs with applications"]}]}],"canonical_facts":{"dc:contributor.advisor":["Qiu, Jinniao"],"dc:contributor.committeemember":["Ware, Antony Frank","Swishchuk, Anatoliy V."],"dc:creator":["Molla, Md Hasib Uddin"],"dc:date":["2020-11"],"dc:date.accessioned":["2020-09-11T22:31:22Z"],"dc:date.available":["2020-09-11T22:31:22Z"],"dc:date.issued":["2020-09-10"],"dc:description.abstract":["We introduce a new scheme combining the finite element method and machine learning techniques for the numerical approximations of coupled forward-backward stochastic partial differential equations (FBSPDEs) with homogeneous Dirichlet boundary conditions. For the FBSPDE, the finite element method in the spatial domain leads to approximations by finite-dimensional forward-backward stochastic differential equations (FBSDEs) in the temporal domain. We then approximate the solution of FBSDE by some existing machine learning schemes. Strong convergence results for spatial discretization of FBSPDEs are addressed."],"dc:identifier.doi":["http://dx.doi.org/10.11575/PRISM/38185"],"dc:identifier.uri":["http://hdl.handle.net/1880/112515"],"dc:language.iso":["eng"],"dc:publisher.institution":["University of Calgary"],"dc:rights":["University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission."],"dc:subject":["Stochastic partial differential equations","deep learning"],"dc:title":["Numerical approximations of coupled forward-backward SPDEs with applications"],"dc:type":["master thesis"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_name":["Master of Science (MSc)"],"thesis:institution_name":["University of Calgary"]},"updated_at":"2026-07-24T01:30:13Z"}