In fish modeling, a significant amount of uncertainty exists in the parameter values, parameterizations, functional form of model equations, and even the state variables themselves. This is due to the complexity and lack of understanding of the processes involved, as well as the measurement sparsity. These challenges motivate the present proof-of-concept study to simultaneously learn and estimate the state variables, parameters, and model equations from sparse observations. We employ a novel dynamics-based Bayesian learning framework for high-dimensional, coupled fish-biogeochemical-physical partial-differential equations (PDEs) models, allowing the simultaneous inference of the augmented state variables and parameters. After reviewing the status of ecosystem modeling in the coastal oceans, we first complete a series of PDE-based learning experiments that showcase capabilities for fish-biogeochemical-physical model equations and parameters, using nonhydrostatic Boussinesq flows past a seamount. We then showcase realistic ocean primitive-equation simulations and analyses, using fish catch data  for the Lakshadweep islands in India. These modeling and learning efforts could improve fisheries management from a standpoint of sustainability and efficiency.

To cleanup marine plastics, accurate modeling is needed. We outline and illustrate a new partial-differential-equation methodology for characterizing and modeling plastic transports in time and space (4D), showcasing results for Massachusetts Bay. We couple our primitive equation model for ocean dynamics with our composition based advection for Lagrangian transport. We show that the ocean physics predictions have skill by comparison with synoptic data. We predict the fate of plastics originating from four sources: rivers, beach and nearshore, local Bay, and remote offshore. We analyze the transport patterns and the regions where plastics accumulate, comparing results with and without plastic settling. Simulations agree with existing debris and plastics data. They also show new results: (i) Currents set-up by wind events strongly affect floating plastics. Winds can for example prevent Merrimack outflows reaching the Bay; (ii) There is significant chaotic stirring between nearshore and offshore floating plastics as explained by ridges of Lagrangian Coherent Structures (LCSs); (iii) With 4D plastic motions and settling, plastics from the Merrimack and nearshore regions can settle to the seabed before offshore advection; (iv) Internal waves and tides can bring plastics downward and out of main currents, leading to settling to the deep bottom. (v) Attractive LCSs ridges are frequent in the northern Cape Cod Bay, west of the South Shore, and southern Stellwagen Bank. They lead to plastic accumulation and sinking along thin subduction zones.