标题： 极端稀疏下的海洋动力学生成拉格朗日数据同化 显示英文标题

标题： Generative Lagrangian data assimilation for ocean dynamics under extreme sparsity

摘要： 从观测数据中重建海洋动力学本质上受到空间采样稀疏、不规则和拉格朗日性质的限制，特别是在次表层和偏远区域。 这种稀疏性对预测涡旋脱落和 rogue waves 等关键现象构成了重大挑战。 传统数据同化方法和深度学习模型在这些约束下往往难以恢复中尺度湍流。 我们利用一种结合神经算子和去噪扩散概率模型（DDPMs）的深度学习框架，从极其稀疏的拉格朗日观测中重建高分辨率的海洋状态。 通过将生成模型条件设置为神经算子的输出，该框架即使在$99\%$稀疏度（对于合成数据）和$99.9\%$稀疏度（对于真实卫星观测）下也能准确捕捉小尺度、高波数的动力学。 我们在基准系统、合成浮标观测和真实卫星数据上验证了我们的方法，与其它深度学习基线方法相比，展示了在严重空间采样限制下的鲁棒性能。 显示英文摘要

摘要： Reconstructing ocean dynamics from observational data is fundamentally limited by the sparse, irregular, and Lagrangian nature of spatial sampling, particularly in subsurface and remote regions. This sparsity poses significant challenges for forecasting key phenomena such as eddy shedding and rogue waves. Traditional data assimilation methods and deep learning models often struggle to recover mesoscale turbulence under such constraints. We leverage a deep learning framework that combines neural operators with denoising diffusion probabilistic models (DDPMs) to reconstruct high-resolution ocean states from extremely sparse Lagrangian observations. By conditioning the generative model on neural operator outputs, the framework accurately captures small-scale, high-wavenumber dynamics even at $99\%$ sparsity (for synthetic data) and $99.9\%$ sparsity (for real satellite observations). We validate our method on benchmark systems, synthetic float observations, and real satellite data, demonstrating robust performance under severe spatial sampling limitations as compared to other deep learning baselines.