{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/79265"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/79265","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Bayesian inference of stochastic dynamical models","abstract":"A new methodology for Bayesian inference of stochastic dynamical models is developed. The methodology leverages the dynamically orthogonal (DO) evolution equations for reduced-dimension uncertainty evolution and the Gaussian mixture model DO filtering algorithm for nonlinear reduced-dimension state variable inference to perform parallelized computation of marginal likelihoods for multiple candidate models, enabling efficient Bayesian update of model distributions. The methodology also employs reduced-dimension state augmentation to accommodate models featuring uncertain parameters. The methodology is applied successfully to two high-dimensional, nonlinear simulated fluid and ocean systems. Successful joint inference of an uncertain spatial geometry, one uncertain model parameter, and [Omicron](105) uncertain state variables is achieved for the first. Successful joint inference of an uncertain stochastic dynamical equation and [Omicron](105) uncertain state variables is achieved for the second. Extensions to adaptive modeling and adaptive sampling are discussed.","abstract_html":"A new methodology for Bayesian inference of stochastic dynamical models is developed. The methodology leverages the dynamically orthogonal (DO) evolution equations for reduced-dimension uncertainty evolution and the Gaussian mixture model DO filtering algorithm for nonlinear reduced-dimension state variable inference to perform parallelized computation of marginal likelihoods for multiple candidate models, enabling efficient Bayesian update of model distributions. The methodology also employs reduced-dimension state augmentation to accommodate models featuring uncertain parameters. The methodology is applied successfully to two high-dimensional, nonlinear simulated fluid and ocean systems. Successful joint inference of an uncertain spatial geometry, one uncertain model parameter, and [Omicron](105) uncertain state variables is achieved for the first. Successful joint inference of an uncertain stochastic dynamical equation and [Omicron](105) uncertain state variables is achieved for the second. Extensions to adaptive modeling and adaptive sampling are discussed.","abstract_has_math":false,"creators":["Lu, Peter Guang Yi"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Mechanical Engineering.","school":null,"contributors":[],"advisors":["Pierre F.J. Lermusiaux."],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013","date_published":"2013","updated_at":"2026-07-22T22:21:23Z","subjects":["Mechanical Engineering."],"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/1721.1/79265","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Pierre F.J. Lermusiaux."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Department of Mechanical Engineering."]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. Department of Mechanical Engineering."]},{"key":"dc:creator","label":"Author","values":["Lu, Peter Guang Yi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2013-06-17T19:51:45Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2013-06-17T19:51:45Z"]},{"key":"dc:date.issued","label":"Date","values":["2013"]},{"key":"dc:publisher","label":"Institution","values":["Massachusetts Institute of Technology"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mechanical Engineering."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["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."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/79265"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2013.","Cataloged from PDF version of thesis.","Includes bibliographical references (p. 165-175)."]},{"key":"dc:description.abstract","label":"Abstract","values":["A new methodology for Bayesian inference of stochastic dynamical models is developed. The methodology leverages the dynamically orthogonal (DO) evolution equations for reduced-dimension uncertainty evolution and the Gaussian mixture model DO filtering algorithm for nonlinear reduced-dimension state variable inference to perform parallelized computation of marginal likelihoods for multiple candidate models, enabling efficient Bayesian update of model distributions. The methodology also employs reduced-dimension state augmentation to accommodate models featuring uncertain parameters. The methodology is applied successfully to two high-dimensional, nonlinear simulated fluid and ocean systems. Successful joint inference of an uncertain spatial geometry, one uncertain model parameter, and [Omicron](105) uncertain state variables is achieved for the first. Successful joint inference of an uncertain stochastic dynamical equation and [Omicron](105) uncertain state variables is achieved for the second. Extensions to adaptive modeling and adaptive sampling are discussed."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:title","label":"Title","values":["Bayesian inference of stochastic dynamical models"]}]}],"canonical_facts":{"dc:contributor.advisor":["Pierre F.J. Lermusiaux."],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Mechanical Engineering."],"dc:contributor.other":["Massachusetts Institute of Technology. Department of Mechanical Engineering."],"dc:creator":["Lu, Peter Guang Yi"],"dc:date.accessioned":["2013-06-17T19:51:45Z"],"dc:date.available":["2013-06-17T19:51:45Z"],"dc:date.issued":["2013"],"dc:description":["Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2013.","Cataloged from PDF version of thesis.","Includes bibliographical references (p. 165-175)."],"dc:description.abstract":["A new methodology for Bayesian inference of stochastic dynamical models is developed. The methodology leverages the dynamically orthogonal (DO) evolution equations for reduced-dimension uncertainty evolution and the Gaussian mixture model DO filtering algorithm for nonlinear reduced-dimension state variable inference to perform parallelized computation of marginal likelihoods for multiple candidate models, enabling efficient Bayesian update of model distributions. The methodology also employs reduced-dimension state augmentation to accommodate models featuring uncertain parameters. The methodology is applied successfully to two high-dimensional, nonlinear simulated fluid and ocean systems. Successful joint inference of an uncertain spatial geometry, one uncertain model parameter, and [Omicron](105) uncertain state variables is achieved for the first. Successful joint inference of an uncertain stochastic dynamical equation and [Omicron](105) uncertain state variables is achieved for the second. Extensions to adaptive modeling and adaptive sampling are discussed."],"dc:description.degree":["S.M."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/79265"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc: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."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Mechanical Engineering."],"dc:title":["Bayesian inference of stochastic dynamical models"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:21:23Z"}