This thesis demonstrates the use of exact equations to predict time-optimal mission plans for a marine vehicle that visits a number of locations in a given dynamic ocean current field. The missions demonstrated begin and end in the same location and visit a finite number of locations or waypoints in the minimal time; this problem bears close resemblance to that of the classic “traveling salesman,” albeit with the added complexity of a continuously changing flow field. The paths, or “legs,” between all goal waypoints are generated by numerically solving exact time-optimal path planning level-set differential equations. The equations grow a reachability front from the starting location in all directions. Whenever the front reaches a waypoint, a new reachability front is immediately started from that location. This process continues until one set of reachability fronts has reached all goal waypoints and has returned to the original location. The time-optimal path for the entire mission is then obtained by trajectory backtracking, going through the optimal set of reachability fields in reverse order. Due to the spatial and temporal dynamics, a varying start time results in different paths and durations for each leg and requires all permutations of travel to be calculated. Even though the method is very efficient and the optimal path can be computed serially in real-time for common naval operations, for additional computational speed, a high-performance computing cluster was used to solve the level set calculations in parallel. This method is first applied to several hypothetical missions. The method and distributed computational solver are then validated for naval applications using an operational multi-resolution ocean modeling system of real-world current fields for the complex Philippines Archipelago region. Because the method calculates the global optimum, it serves two purposes. It can be used in its present form to plan multi-waypoint missions offline in conjunction with a predictive ocean current modeling system, or it can be used as a litmus test for approximate future solutions to the traveling salesman problem in dynamic flow fields.

Abstract: The data assimilation community has developed a variety of strategies for the blending of observations and models, taking into account their inherent uncertainties. It has offered persuasive arguments for its utility in some applications. For example, in weather forecasting and subsurface hydrology. I will focus on Bayesian methodologies, and describe a few new data assimilation strategies that take advantage of computational and physical conditions inherent in the intended application in order to provide useful alternative forecasts (estimates).

Biography: Juan M. Restrepo is Professor of Mathematics at Oregon State University. He holds courtesy appointments in the College of Engineering as well as the College of Earth, Oceans and Atmospheric Sciences. His research interests straddle computational data-driven and probabilistic methods and multi-scale dynamics. The applications emphasize ocean dynamics and transport. The recipient of a DOE Young Investigator award, and the SIAM Geoscience Career Award. He’s a fellow of SIAM.

The ocean twilight zone, or mesopelagic zone, spans ocean depths from approximately 200 to 1,000 meters and forms one of the largest habitats on Earth. The twilight zone is home to diverse communities of zooplankton and micronekton, yet relatively little is known about their biology, adaptations, abundance, biomass, or distribution. Recent acoustic inferences suggest that the global biomass estimates of fish in the mesopelagic zone based on net sampling may be an order of magnitude too low. Furthermore, many twilight zone inhabitants participate in daily vertical migration, likely the largest migration that occurs on earth, and play a previously underappreciated role in Earth’s climate, helping to control the rate at which the ocean absorbs atmospheric carbon dioxide and transfers it to the deep ocean. However, there is a current technological void for characterizing mesopelagic ecosystems. On April 11, 2018, the Woods Hole Oceanographic Institution was awarded $35 million by the Audacious Project, a new philanthropic collaboration housed at TED, to explore the Ocean Twilight Zone. This talk is aimed at presenting the first wave of new sensors and platforms currently under development at WHOI to enable exploration of the Ocean Twilight Zone. Specifically, this talk will focus on the Deep-See system, which involves a combination of acoustical, optical and genetic sampling systems for ecosystem assessment. This instrument is particularly well suited to understanding the diverse communities of zooplankton and micronekton in relation to environmental variability, such as meso-scale oceanic eddies, fronts, and upwelling regions, and abrupt topography, such as canyons, seamounts, and shelf breaks. Impacts from this research will extend from basic research problems underpinning science-based fisheries management and decision making, to broader societally relevant problems.

Congratulations to Deepak Subramani on his graduation! Deepak received a PhD from Mechanical Engineering for his research on “Probabilistic Regional Ocean Predictions: Stochastic Fields and Optimal Planning” with our MSEAS group at MIT.

Congratulations to Corbin Foucart and Abhinav Gupta for successfully clearing the MIT Mechanical Engineering Ph.D Qualifying Exams. They now begin their journey towards outstanding Ph.D theses. All the best!