{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/101624"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/101624","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Modeling and inference of the dynamics of spatiotemporally evolving systems using evolving gaussian processes","abstract":"In this work, we present a new differentially-constrained machine learning model, termed Evolving Gaussian Processes (E-GP), for modeling and inference of spatiotemporally evolving dynamical systems. We show that an E-GP model can be used to estimate the latent state of large-scale physical systems of this type, and furthermore that a single E-GP model can generalize over multiple physically-similar systems over a range of parameters using only a few training sets. It is also shown that an E-GP model provides access to practical physical insights into the dynamic structure of the system(s) it is trained on. In particular, from spectral analysis of the linear dynamic layer in the top level of the E-GP model, one may derive the Koopman modes and eigenvalues of the system. We are also able to derive the spatial distribution of the invariant subspaces of a system using a new clustering method. This information can be used for sensor placement and/or mobile agent path planning for robust inference of the state of the system using few measurements. We primarily demonstrate our method on computational flow dynamics (CFD) data sets on fluid flowing past a cylinder at different Reynolds numbers. Though these systems are governed by highly nonlinear partial differential equations (the Navier-Stokes equations), we show that their major dynamical modes can be captured by a linear dynamical layer over the temporal evolution of the weights of stationary kernels.","abstract_html":"In this work, we present a new differentially-constrained machine learning model, termed Evolving Gaussian Processes (E-GP), for modeling and inference of spatiotemporally evolving dynamical systems. We show that an E-GP model can be used to estimate the latent state of large-scale physical systems of this type, and furthermore that a single E-GP model can generalize over multiple physically-similar systems over a range of parameters using only a few training sets. It is also shown that an E-GP model provides access to practical physical insights into the dynamic structure of the system(s) it is trained on. In particular, from spectral analysis of the linear dynamic layer in the top level of the E-GP model, one may derive the Koopman modes and eigenvalues of the system. We are also able to derive the spatial distribution of the invariant subspaces of a system using a new clustering method. This information can be used for sensor placement and/or mobile agent path planning for robust inference of the state of the system using few measurements. We primarily demonstrate our method on computational flow dynamics (CFD) data sets on fluid flowing past a cylinder at different Reynolds numbers. Though these systems are governed by highly nonlinear partial differential equations (the Navier-Stokes equations), we show that their major dynamical modes can be captured by a linear dynamical layer over the temporal evolution of the weights of stationary kernels.","abstract_has_math":false,"creators":["Whitman, Joshua Earl"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Chowdhary, Girish"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-09-27T16:18:02Z","date_published":"2018-09-27T16:18:02Z","updated_at":"2026-07-22T22:24:40Z","subjects":["Dynamics","Machine Learning","Computational Flow Dynamics","Gaussian Process"],"languages":["en"],"rights":["Copyright 2018 by Joshua Whitman"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/101624","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Chowdhary, Girish"]},{"key":"dc:creator","label":"Author","values":["Whitman, Joshua Earl"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-09-27T16:18:02Z","2018-07-19","2018-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Dynamics","Machine Learning","Computational Flow Dynamics","Gaussian Process"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2018 by Joshua Whitman"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/101624"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this work, we present a new differentially-constrained machine learning model, termed Evolving Gaussian Processes (E-GP), for modeling and inference of spatiotemporally evolving dynamical systems. We show that an E-GP model can be used to estimate the latent state of large-scale physical systems of this type, and furthermore that a single E-GP model can generalize over multiple physically-similar systems over a range of parameters using only a few training sets. It is also shown that an E-GP model provides access to practical physical insights into the dynamic structure of the system(s) it is trained on. In particular, from spectral analysis of the linear dynamic layer in the top level of the E-GP model, one may derive the Koopman modes and eigenvalues of the system. We are also able to derive the spatial distribution of the invariant subspaces of a system using a new clustering method. This information can be used for sensor placement and/or mobile agent path planning for robust inference of the state of the system using few measurements. We primarily demonstrate our method on computational flow dynamics (CFD) data sets on fluid flowing past a cylinder at different Reynolds numbers. Though these systems are governed by highly nonlinear partial differential equations (the Navier-Stokes equations), we show that their major dynamical modes can be captured by a linear dynamical layer over the temporal evolution of the weights of stationary kernels.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-09-27 without embargo terms","The student, Joshua Whitman, accepted the attached license on 2018-07-19 at 11:28.","The student, Joshua Whitman, submitted this Thesis for approval on 2018-07-19 at 11:36.","This Thesis was approved for publication on 2018-07-19 at 14:38.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12938 on 2018-09-27 at 10:50:14","Made available in DSpace on 2018-09-27T16:18:02Z (GMT). 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We show that an E-GP model can be used to estimate the latent state of large-scale physical systems of this type, and furthermore that a single E-GP model can generalize over multiple physically-similar systems over a range of parameters using only a few training sets. It is also shown that an E-GP model provides access to practical physical insights into the dynamic structure of the system(s) it is trained on. In particular, from spectral analysis of the linear dynamic layer in the top level of the E-GP model, one may derive the Koopman modes and eigenvalues of the system. We are also able to derive the spatial distribution of the invariant subspaces of a system using a new clustering method. This information can be used for sensor placement and/or mobile agent path planning for robust inference of the state of the system using few measurements. We primarily demonstrate our method on computational flow dynamics (CFD) data sets on fluid flowing past a cylinder at different Reynolds numbers. Though these systems are governed by highly nonlinear partial differential equations (the Navier-Stokes equations), we show that their major dynamical modes can be captured by a linear dynamical layer over the temporal evolution of the weights of stationary kernels.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-09-27 without embargo terms","The student, Joshua Whitman, accepted the attached license on 2018-07-19 at 11:28.","The student, Joshua Whitman, submitted this Thesis for approval on 2018-07-19 at 11:36.","This Thesis was approved for publication on 2018-07-19 at 14:38.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12938 on 2018-09-27 at 10:50:14","Made available in DSpace on 2018-09-27T16:18:02Z (GMT). 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