Gaussian processes at the Helm(holtz): A more fluid model for ocean currents
This work addresses oceanographers' need for more accurate fluid models, but it is incremental as it builds on existing Gaussian process methods with a domain-specific adaptation.
The authors tackled the problem of reconstructing ocean currents and identifying divergences from sparse buoy velocity observations by proposing a Gaussian process model that incorporates physical properties through a Helmholtz decomposition, achieving improved performance over standard stationary kernels.
Given sparse observations of buoy velocities, oceanographers are interested in reconstructing ocean currents away from the buoys and identifying divergences in a current vector field. As a first and modular step, we focus on the time-stationary case - for instance, by restricting to short time periods. 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 reconstruction 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 with theory and experiments on synthetic and real ocean data.