Gaussian processes at the Helm(holtz): A more fluid model for ocean currents
Name
berlinghieri-renb-sm-eecs-2023-thesis.pdf
Description
Thesis PDF
Size
11.49 MB
Format
Adobe PDF
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Author(s)
Berlinghieri, Renato
Advisor(s)
Broderick, Tamara
Date Issued
June 2023
Publisher
Massachusetts Institute of Technology
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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