Reduced Order Modeling (ROM) for UUV/USV Environmental Awareness -- 19-013

In Phase I, Metron and the University of Miami (UM) propose to develop a theoretic reduction of dynamics framework applicable to the prediction of oceanographic fields in geophysical fluid dynamic models for use onboard unmanned platforms. Our approach leverages, extends and combines modern advances in the renormalization group and Bayesian probability combined with fluid dynamics modeling and forecasting. We will adopt a mathematical procedure called the renormalization group (RG) method from theoretical physics to systematically reduce the dynamics to a simpler representation with a fewer number of degrees of freedom confined to a lower dimensional space. The renormalization group plays a prominent role in modern theoretical physics, especially in dealing with problems that have multiple time or length scales, and is uniquely suited for the reduction of dynamic oceanographic fields. It has applications in many areas such as the reduction of transport equations to fluid dynamics and the analysis of turbulence. The RG based reduced order modeling (ROM) framework is extensible to forecasting the evolution of dynamic fields which is critical for making optimal control decisions.