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 Zia, Tamara Broderick

Keywords: Gaussian processes, Helmholtz decomposition, divergence, vorticity, ocean currents

TL;DR: We put a Gaussian process prior on the two components of the Helmholtz decomposition to model ocean currents.

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 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 ocean data.