Increasingly, autonomous vehicles that optimally collect/harvest external fields from highly dynamic environments have grown in relevance for Planet Earth. This includes path planning for optimal energy harvesting (solar, wind, wave, thermal, etc.) or optimal cleanup or collections in dynamic environments. In this work, we develop an exact partial differential equation-based methodology that predicts collection-time optimal paths for autonomous vehicles navigating in dynamic environments. The governing differential equations solve the multi-objective optimization problem of navigating a vehicle autonomously in a highly dynamic flow field to any destination to minimize travel time while also maximizing the collected amounts of fields harvested by the vehicle. Using Hamilton-Jacobi theory for reachability, our methodology computes the exact set of Pareto optimal solutions to the multi-objective path planning problem. Our approach applies to path planning in various environments; however, we primarily present examples of navigating in dynamic ocean flows. First, we validate our methodology using steady and unsteady benchmark cases. We then showcase optimal fish growth paths for moving fish farms, optimal algae growth and collection paths for autonomous carbon capture, and optimal plastic collection paths for marine cleanup. Overall, we find that our exact planning equations and efficient schemes are promising to address several pressing challenges for our planet.

Our generalized neural closure models (gnCMs) based on unified neural partial differential equations (PDEs) are applied to ocean, sea ice, and chaotic systems. We augment existing/low-fidelity dynamical models directly in their PDE forms with both Markovian and non-Markovian neural network (NN) closures. The melding of the existing models with NNs in the continuous spatiotemporal space followed by numerical discretization automatically allows for generalizability. The Markovian term is designed to enable extraction of its analytical form and thus provides interpretability. The non-Markovian terms allow accounting for inherently missing time delays needed to represent the real world. Our flexible gnCMs provide full autonomy for the design of the unknown closure terms such as using any linear-, shallow-, or deep-NN architectures, selecting the span of the input function libraries, and using either or both Markovian and non-Markovian closure terms, all in accord with prior knowledge. We apply the gnCMs to learning experiments with advecting nonlinear waves, shocks, ocean acidification, ocean submesoscales, and sea ice models. We highlight applications to chaotic systems, emphasizing the need for adaptive learning schemes. Our learned gnCMs discover missing chaotic physics, find leading numerical error terms, discriminate among candidate functional forms in an interpretable fashion, achieve generalization, and compensate for the lack of complexity in simpler models.

Abstract: The New England Seamount Chain in the North Atlantic presents a combination of complex bathymetry and highly dynamic currents due to their location near the Gulf Stream. The Task Force Ocean Biological Soundscapes team have sampled simultaneous ambient noise, biological oceanography, and bio-physical oceanographic sections around the Kelvin Seamount to better understand the impacts of both the seamount bathymetry and Gulf Stream features on the structure of pelagic biology in the water column and physical oceanographic properties. During an October 2023 field campaign on the R/V Langseth, Tropical Storm Phillippe interrupted a research cruise such that oceanographic sections were collected before and after the storm, and water column as well as bottom mounted ambient noise data were recorded before, during, and after the storm. While the storm and periodic ship traffic affect ambient noise levels as historically described by Piggott and Wenz, oceanographic mixing and bio-physical interactions are more complex with Gulf Stream front and eddy dynamics appearing to be more significant drivers than potential mixing associated with the tropical storm passage.