Adaptive Stochastic Reduced Order Modeling for Autonomous Ocean Platforms

Onboard probabilistic forecasting and data assimilation is challenging for unmanned autonomous platforms. Due to the operational constraints, efficient adaptive reduced order models (ROMs) are needed. To extend the duration for which Dynamic Mode Decomposition (DMD) predictions are accurate, we utilize and augment incremental methods that update the reduced order state but also adapt the DMD. Our adaptive ROM methods are dynamic and stochastic. They update the state, parameters, and basis functions, in response to the changing forecasts, possibly computed in remote centers, and to observations made by the autonomous platforms and by other assets. For the latter, to allow learning even when observations are sparse and multivariate, we employ Bayesian data assimilation. Specifically, we extend the Gaussian Mixture Model- Dynamically Orthogonal (GMM-DO) filter to stochastic DMD forecasts and Bayesian GMM updates of the DMD coefficients, state, and parameters, learning from the limited gappy observation data sets.