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

arXiv: https://arxiv.org/abs/2302.10364 · HTML: https://mlsanity.com/paper/2302.10364/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 46 references that are in the map.
- First posted on arXiv 20 Feb 2023.

## Builds on (most cited first, 4 of 4)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately](https://mlsanity.com/paper/2201.10085/) (2022)
- [Modeling and interpolation of the ambient magnetic field by Gaussian processes](https://mlsanity.com/paper/1509.04634/) (2015)

## Built on by (most cited first, 12 of 12)

- [Hodge-Compositional Edge Gaussian Processes](https://mlsanity.com/paper/2310.19450/) (2023)
- [Intrinsic Gaussian Vector Fields on Manifolds](https://mlsanity.com/paper/2310.18824/) (2023)
- [Physics-Informed Variational State-Space Gaussian Processes](https://mlsanity.com/paper/2409.13876/) (2024)
- [OceanBench: The Sea Surface Height Edition](https://mlsanity.com/paper/2309.15599/) (2023)
- [Regularized KL-Divergence for Well-Defined Function-Space Variational Inference in Bayesian neural networks](https://mlsanity.com/paper/2406.04317/) (2024)
- [Discrete Gaussian Vector Fields On Meshes](https://mlsanity.com/paper/2507.20024/) (2025)
- [BALLAST: Bayesian Active Learning with Look-ahead Amendment for Sea-drifter Trajectories under Spatio-Temporal Vector Fields](https://mlsanity.com/paper/2509.26005/) (2025)
- [Generalizable Implicit Neural Representations via Parameterized Latent Dynamics for Baroclinic Ocean Forecasting](https://mlsanity.com/paper/2503.21588/) (2025)
- [Mass Conservation on Rails -- Rethinking Physics-Informed Learning of Ice Flow Vector Fields](https://mlsanity.com/paper/2510.06286/) (2025)
- [Triply-Scalable Equivariant Gaussian Process Modeling](https://mlsanity.com/paper/2609.21085/) (2026)
- [Gaussian Flow Dynamics: Simulation-Free Neural SDE Learning Beyond One-Time Marginals](https://mlsanity.com/paper/2610.04390/) (2026)
- [Ghost tasking for parametrized Gaussian Processes solving linear differential equations](https://mlsanity.com/paper/2610.12009/) (2026)

## Abstract (arXiv)

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.