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Gaussian processes at the Helm(holtz): A better way to model ocean currents
Renato Berlinghieri · Tamara Broderick · Ryan Giordano · Tamay Ozgokmen · Kaushik Srinivasan · Brian Trippe · Junfei Xia

Understanding the behavior of ocean currents has important practical applications. Since we expect current dynamics to be smooth but highly non-linear, Gaussian processes (GPs) offer an attractive model. In particular, one existing approach is to consider the velocities of the buoys as sparse observations of a vector field in two spatial dimensions and one time dimension. But we show that applying a GP, e.g. with a standard square exponential kernel, directly to this data fails to capture real-life current structure, such as continuity of currents and the shape of vortices. By contrast, these physical properties are captured by divergence and curl-free components of a vector field obtained through a Helmholtz decomposition. So we propose instead to model these components with a GP directly. 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 our method on real oceans data.

Author Information

Renato Berlinghieri (MIT)
Renato Berlinghieri

I am a 2nd year PhD student in Computer Science at MIT, working in [LIDS](https://lids.mit.edu) under the supervision of Professor [Tamara Broderick](https://tamarabroderick.com). My main research interests are Bayesian inference and machine learning. My current work focuses on modelling ocean currents using physics-informed Gaussian Processes.

Tamara Broderick (MIT)
Ryan Giordano (MIT)
Tamay Ozgokmen (University of Miami)
Kaushik Srinivasan (UCLA)
Brian Trippe (Columbia University)
Junfei Xia (University of Miami)

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