Lagrangian Drifter Path Identification and Prediction: SINDy vs Neural ODE

In this study, we investigate the performance of the sparse identification of nonlinear dynamics (SINDy) algorithm and the neural ordinary differential equations (ODEs) in identification of the underlying mechanisms of open ocean Lagrangian drifter hydrodynamics with possible applications in coastal and port hydrodynamic processes. With this motivation we employ two different Lagrangian drifter datasets acquired by National Oceanic and Atmospheric Administration (NOAA)'s surface buoys with proper World Meteorological Organization (WMO) numbers. In the SINDy approach, the primary goal is to identify the drifter paths of buoys using ordinary differential equation sets with a minimal number of sparse coefficients. In the neural ODE approach, the goal is to identify the derivative of the hidden state of a neural network (NN). Using the acquired data, we examine the applicability of the SINDy and the neural ODE algorithms in identification of the drifter trajectories comparatively. We propose that while both of the algorithms may give acceptable results for open ocean, the SINDy-based algorithmic approach can predict the Lagrangian drifter paths more accurately and consistently at least for the datasets investigated and parameters selected. A discussion of our findings with potential applications in search and rescue missions in the open ocean, their limitations and applicability are also presented.