Discovering the dynamics of Sargassum rafts' centers of mass

Since 2011, rafts of floating 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 Sargassum forming a raft and the effects of Earth's rotation. In practical applications, the motion of the centers of mass of the rafts is what matters; however, the law of motion remains undetermined in closed form, making a strong case for using machine learning to develop a low-dimensional model that enables numerical efficiency and facilitates conceptual understanding. In this exploratory work, 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. Overall, the LSTM and SINDy models perform similarly, both operating better with tightly connected rafts but lose precision in more complex scenarios, such as wind effects and loosely connected rafts. LSTM is more effective with simple designs, utilizing fewer neurons and layers, but lacks interpretability, unlike SINDy, which identifies explicit functional dependencies. Including windowed velocity terms enhances modeling of nonlocal interactions, particularly in data sets with sparsely connected rafts.