Gaussian processes at the Helm(holtz): A more fluid model for ocean currents
Renato Berlinghieri, Brian L. Trippe, David R. Burt, Ryan James Giordano, Kaushik Srinivasan, Tamay Özgökmen, Junfei Xia, Tamara Broderick
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.
