Adaptive Sampling for the Coastal Ocean

We present a novel methodology for adaptive sampling in the coastal ocean that exploits the governing nonlinear ocean dynamics and captures the non-Gaussian structure of the stochastic state fields. Optimal observation locations are determined by maximizing the mutual information between the candidate observations and the variables of interest. We develop a novel Bayesian smoother for high-dimensional continuous stochastic fields governed by general nonlinear dynamics. This smoother combines the adaptive reduced-order Dynamically-Orthogonal equations with Gaussian Mixture Models, extending linearized Gaussian backward pass updates to a nonlinear, non-Gaussian setting. The Bayesian information transfer, both forward and backward in time, is efficiently carried out in the evolving dominant stochastic subspace. Building on the foundations of the smoother, we then derive an efficient technique to quantify the spatially and temporally varying mutual information field in general nonlinear dynamical systems. The globally optimal sequence of future sampling locations is rigorously determined by a novel dynamic programming approach that combines this computation of mutual information fields with the predictions of the forward reachable set. All the results are exemplified and their performance is quantitatively assessed using a variety of simulated fluid and ocean flows.