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Gaussian processes at the Helm(holtz): A more fluid model for ocean currents

Renato Berlinghieri · Brian Trippe · David Burt · Ryan Giordano · Kaushik Srinivasan · Tamay Özgökmen · Junfei Xia · Tamara Broderick

Exhibit Hall 1 #214


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 dynamics to be smooth but highly non-linear, 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 oceans data.

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