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oai:dspace.mit.edu:1721.1/1513852023-08-01T03:02:19Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023

Broderick, Tamara Berlinghieri, Renato Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science 2023-07-31T19:35:45Z 2023-07-31T19:35:45Z 2023-06 2023-07-13T14:16:08.253Z https://hdl.handle.net/1721.1/151385 Oceanographers are interested in predicting ocean currents and identifying divergences in a current vector field based on sparse observations of buoy velocities. Since we expect current velocity to be a continuous but highly non-linear function of spatial location, Gaussian processes (GPs) offer an attractive model. But we show that applying a GP with a standard stationary kernel directly to buoy data can struggle at both current prediction and divergence identification – due to some physically unrealistic prior assumptions. To better reflect known physical properties of currents, we propose to instead put a standard stationary kernel on the divergence and curl-free components of a vector field obtained through a Helmholtz decomposition. We show that, because this decomposition relates to the original vector field just via mixed partial derivatives, we can still perform inference given the original data with only a small constant multiple of additional computational expense. We illustrate the benefits of our method on synthetic and real ocean data. S.M. Massachusetts Institute of Technology In Copyright - Educational Use Permitted Copyright retained by author(s) https://rightsstatements.org/page/InC-EDU/1.0/ Gaussian processes at the Helm(holtz): A more fluid model for ocean currents Thesis application/pdf Master Master of Science in Electrical Engineering and Computer Science Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="f5173233-c31b-48eb-a8bc-c56f06f9fc74"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Title>Gaussian processes at the Helm(holtz): A more fluid model for ocean currents</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2023-06</PublicationDate> <Authors> <Author> <DisplayName>Berlinghieri, Renato</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>https://rightsstatements.org/page/InC-EDU/1.0/</License> <Abstract>Oceanographers are interested in predicting ocean currents and identifying divergences in a current vector field based on sparse observations of buoy velocities. Since we expect current velocity to be a continuous but highly non-linear function of spatial location, Gaussian processes (GPs) offer an attractive model. But we show that applying a GP with a standard stationary kernel directly to buoy data can struggle at both current prediction and divergence identification – due to some physically unrealistic prior assumptions. To better reflect known physical properties of currents, we propose to instead put a standard stationary kernel on the divergence and curl-free components of a vector field obtained through a Helmholtz decomposition. We show that, because this decomposition relates to the original vector field just via mixed partial derivatives, we can still perform inference given the original data with only a small constant multiple of additional computational expense. We illustrate the benefits of our method on synthetic and real ocean data.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>