Discovering the dynamics of \emph{Sargassum} rafts' centers of mass

TL;DR

This study compares machine learning models, LSTM and SINDy, for predicting the movement of Sargassum rafts' centers of mass, emphasizing the importance of physics-inspired features and model interpretability.

Contribution

It introduces a physics-informed approach to model raft dynamics, contrasting black-box and transparent models, and highlights the effectiveness of windowed velocity features for nonlocal interactions.

Findings

LSTM outperforms SINDy in simple conditions with fewer neurons.

SINDy provides explicit functional relationships, enhancing interpretability.

Model accuracy declines with increased raft complexity and environmental effects.

Abstract

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.