arXiv:2507.18771nlin.CDcs.LG2025-07

用机器学习预测海藻浮筏质心运动,结合物理模型提升预测精度。

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

  • 基于eBOMB物理模型构建神经网络与稀疏识别方法
  • 紧密连接的浮筏预测效果最佳,风力影响下精度下降
  • SINDy模型可解释性强,适合需要机制分析的研究者

自2011年以来,浮游海藻浮筏频繁阻塞美洲间海域海岸。浮筏运动表现为高维非线性动力系统。本文提出的eBOMB模型在Maxey-Riley方程基础上,引入海藻团块间相互作用及地球自转效应。由于缺乏质心运动的预测规律,亟需机器学习方法。本文对比评估了长短期记忆(LSTM)循环神经网络与稀疏非线性动力学识别(SINDy)方法。两者均采用基于eBOMB变量的物理启发闭包建模策略:LSTM学习eBOMB变量到浮筏质心与海流速度差值的映射;SINDy候选函数库由eBOMB变量启发,包含考虑远场输运效应的加窗速度项。两种模型在紧密连接的浮筏中表现最佳,复杂条件下(如风扰动、松散连接)精度下降。LSTM在结构简单时效果更优,但为黑箱模型;而SINDy通过函数库揭示显式关系,具有可解释性。加窗速度项的引入有效建模了非局部相互作用,尤其在稀疏连接的浮筏数据集上表现优异。

原文摘要 · Abstract (English)

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.

海藻监测机器学习非线性动力学海洋科学

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