Discovering the dynamics of \emph{Sargassum} rafts' centers of mass
This work addresses the problem of forecasting Sargassum raft movements for coastal management in the Intra-Americas Seas, but it is incremental as it applies existing machine learning methods to a specific domain.
The paper tackled predicting the motion of Sargassum seaweed rafts, a high-dimensional nonlinear dynamical system, by evaluating LSTM and SINDy models with physics-inspired closures, finding that LSTM performed best in simple designs with fewer neurons and hidden layers, while SINDy offered interpretability through explicit functional relationships.
Since 2011, rafts of floating \emph{Sargassum} seaweed have frequently obstructed the coasts of the Intra-Americas Seas. The motion of the rafts is represented by a high-dimensional nonlinear dynamical system. Referred to as the eBOMB model, this builds on the Maxey--Riley equation by incorporating interactions between clumps of \emph{Sargassum} forming a raft and the effects of Earth's rotation. The absence of a predictive law for the rafts' centers of mass suggests a need for machine learning. In this paper, we evaluate and contrast Long Short-Term Memory (LSTM) Recurrent Neural Networks (RNNs) and Sparse Identification of Nonlinear Dynamics (SINDy). In both cases, a physics-inspired closure modeling approach is taken rooted in eBOMB. Specifically, the LSTM model learns a mapping from a collection of eBOMB variables to the difference between raft center-of-mass and ocean velocities. The SINDy model's library of candidate functions is suggested by eBOMB variables and includes windowed velocity terms incorporating far-field effects of the carrying flow. Both LSTM and SINDy models perform most effectively in conditions with tightly bonded clumps, despite declining precision with rising complexity, such as with wind effects and when assessing loosely connected clumps. The LSTM model delivered the best results when designs were straightforward, with fewer neurons and hidden layers. While LSTM model serves as an opaque black-box model lacking interpretability, the SINDy model brings transparency by discerning explicit functional relationships through the function libraries. Integration of the windowed velocity terms enabled effective modeling of nonlocal interactions, particularly in datasets featuring sparsely connected rafts.