BALLAST: Bayesian Active Learning with Look-ahead Amendment for Sea-drifter Trajectories under Spatio-Temporal Vector Fields

TL;DR

This work tackles learning time-dependent ocean vector fields by optimally placing Lagrangian drifters. It introduces BALLAST, a Bayesian active-learning framework that uses a spatio-temporal Helmholtz GP surrogate and look-ahead trajectory simulations to evaluate information gain, addressing the inadequacy of standard EIG which neglects drifter dynamics. A key contribution is a computationally efficient posterior sampling method via the SPDE approach, enabling tractable look-ahead across multiple posterior field samples. Empirical results on synthetic Temporal Helmholtz fields and a high-fidelity SUNTANS model show BALLAST consistently improves deployment efficiency and reduces required observations, highlighting its practical potential for oceanographic sensing and field inference.

Abstract

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.

Figures (10)

• Figure 1: Illustration of spatio-temporal GP regression of Lagrangian trajectories. The top row shows the aggregated observations at different times. The bottom row shows the regressed GP marginals at corresponding times, where the posterior mean is plotted with colours following entropies of the respective random vectors.
• Figure 2: Deployment comparison under the uniform policy (left), EIG (middle), and our proposed BALLAST (right). Ten Lagrangian observers are placed sequentially, with their placement locations in blue. The observations are plotted with varying brightness according to the observation time (later is brighter).
• Figure 3: The schematic diagram illustrating the BALLAST algorithm for active learning. Given existing observations (top left), we first regress them using a GP (bottom left) and draw multiple samples from the posterior GP (middle). Hypothesised observation trajectories from candidate placements are simulated using sampled fields (top right), which are aggregated for utility computation (bottom right) to select the optimal deployment location (green cross in the bottom right plot).
• Figure 4: Percentage utility gap with 2 standard error bounds of Uniform, EIG, and BALLAST decisions over posterior sample number $J$ at decision times $t = 3, 5, 7$. A percentage utility gap cut-off at $1\%$ is selected with their corresponding $J$ values indicated in text.
• Figure 5: Vector fields at selected time slices of the SUNTANS dataset of rayson2021seasonal.

Theorems & Definitions (6)

• Proposition 1: Informal
• Proposition 2: Formalisation of Prop \ref{['prop:pitfall_naive_AL']}
• proof
• Proposition 3
• proof
• Proposition 4