Dhamma Kimpara (he/him) (Jul 27 2023 at 21:08): Dhamma Kimpara (he/him) (Jul 27 2023 at 21:08):Gaussian Processes at the Helm(holtz): A More Fluid Model for Ocean Currents
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.
Dhamma Kimpara (he/him) (Jul 28 2023 at 21:03):Reliable coarse-grained turbulent simulations through combined offline learning and neural emulation
Integration of machine learning (ML) models of unresolved dynamics into numerical simulations of fluid dynamics has been demonstrated to improve the accuracy of coarse resolution simulations. However, when trained in a purely offline mode, integrating ML models into the numerical scheme can lead to instabilities. In the context of a 2D, quasi-geostrophic turbulent system, we demonstrate that including an additional network in the loss function, which emulates the state of the system into the future, produces offline-trained ML models that capture important subgrid processes, with improved stability properties.
Last updated: May 16 2025 at 17:14 UTC