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Reduced Order Modeling for Stochastic Prediction Onboard Autonomous Platforms at Sea

Heuss, J.P., P.J. Haley, Jr., C. Mirabito, E. Coelho, M.C. Schönau, K. Heaney, and P.F.J. Lermusiaux, 2020. Reduced Order Modeling for Stochastic Prediction Onboard Autonomous Platforms at Sea. In: OCEANS '20 IEEE/MTS, 5-30 October 2020, sub-judice.

For autonomous unmanned platforms at sea, assessing the regional uncertainties and predicting the likely scenarios for the maritime environment around the platforms is a grand challenge. In light of the high dimensionality of ocean models and of the limited observations, such a probabilistic prediction would indeed be most useful (Lermusiaux, 2006; Lermusiaux et al., 2006). Due to the operational constraints including onboard power and space limitations, new efficient stochastic reduced order models (ROMs) are needed for onboard predictions. The regional stochastic ROMs could then learn and assimilate information from both remote comprehensive probabilistic ocean forecasts and sparse measurements made by the platforms.

To initiate this research, we first investigated several Dynamic Mode Decomposition (DMD) methods (Kutz et al., 2016 and references therein) for onboard regional ocean predictions. DMD methods commonly utilize a set of fixed-time snapshots from a single simulation or data set over a period of time, and reduce this set of snapshots to the dynamic modes. The modes are then utilized to forecast further in time from the knowledge of a new initial condition. Two challenges with classic DMD methods are that DMDs are not commonly coupled with a dynamical model (e.g., the original ocean PDEs) and do not commonly account for uncertainty. The reduced-order dynamically-orthogonal (DO) differential equations approach however directly works with the ocean PDEs and optimizes the instantaneous accuracy of the uncertainty representation (Sapsis and Lermusiaux, 2009; Feppon and Lermusiaux, 2018a,b). Our long-term research objective is thus to combine DMD ideas of time-space reductions with reduced-order DO ideas, so as to achieve adaptive reduced-order stochastic predictions for onboard autonomous platforms.

In what follows, we first briefly describe each of the DMD methods we have evaluated. We then showcase some of their results as applied to a 300-member set of ensemble forecasts from the POSYDON-POINT experiment in the Middle Atlantic – New York Bight region for the period 23-27 August 2018 as well as to a 42-day data-driven reanalysis from the Shallow-Water 06 experiment in the Middle Atlantic Bight region for the period 14 August to 24 September 2006. Finally, we utilize these results for use by simulated underwater vehicles in uncertain scenarios, initiating the combination of DMD and DO ideas.