用贝叶斯方法优化海洋漂流器布设，提升矢量场预测精度
BALLAST: Bayesian Active Learning with Look-ahead Amendment for Sea-drifter Trajectories under Spatio-Temporal Vector Fields
- 基于时空高斯过程，考虑漂移器未来轨迹进行前瞻性选址
- 在合成与真实洋流模型上显著优于传统布设策略
- 适合海洋监测、环境建模等需要高效观测部署的场景
我们提出一种形式化的主动学习方法，用于指导拉格朗日观测器在随时间变化的矢量场中布设位置，以推断海洋流场——这是海洋学、海洋科学和海洋工程中的关键任务。现有布设方案多采用标准的‘空间填充’设计或依赖经验判断。主要挑战在于，拉格朗日观测器会随矢量场持续漂移，导致测量位置随时间和空间动态变化，因此必须预估候选布设点的未来轨迹以评估其价值。为此，我们提出BALLAST：贝叶斯主动学习带前瞻修正的海漂器轨迹优化方法。在合成数据和高保真洋流模型上，使用BALLAST的序列布设策略均表现出显著优势。此外，我们还开发了一种新型高斯过程推断方法——原始SPDE交换（VaSE），可大幅提升后验采样效率，该方法亦具有独立研究价值。
原文摘要 · Abstract (English)
We introduce a formal active learning methodology for guiding the placement of Lagrangian observers to infer time-dependent vector fields -- a key task in oceanography, marine science, and ocean engineering -- using a physics-informed spatio-temporal Gaussian process surrogate model. The majority of existing placement campaigns either follow standard `space-filling' designs or relatively ad-hoc expert opinions. A key challenge to applying principled active learning in this setting is that Lagrangian observers are continuously advected through the vector field, so they make measurements at different locations and times. It is, therefore, important to consider the likely future trajectories of placed observers to account for the utility of candidate placement locations. To this end, we present BALLAST: Bayesian Active Learning with Look-ahead Amendment for Sea-drifter Trajectories. We observe noticeable benefits of BALLAST-aided sequential observer placement strategies on both synthetic and high-fidelity ocean current models. In addition, we developed a novel GP inference method -- the Vanilla SPDE Exchange (VaSE) -- to boost the GP posterior sampling efficiency, which is also of independent interest.
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