Dynamic Data-driven Deformable Reduced Models for Coherent Fluids1

AbstractIn autonomous mapping of geophysical fluids, a DDDAS framework involves reduced models constructed offline for online use. Here we show that classical model reduction is ill-suited to deal with model errors manifest in coherent fluids as feature errors including position, scale, shape or other deformations. New fluid representations are required. We propose augmenting amplitude vector spaces by non-parametric deformation vector fields which enables the synthesis of new Principal Appearance and Geometry modes, Coherent Random Field expansions, and an Adaptive Reduced Order Model by Alignment (AROMA) framework. AROMA dynamically deforms reduced models in response to feature errors. It provides robustness and efficiency in inference by unifying perceptual and physical representations of coherent fluids that to the best of our knowledge has not hitherto been proposed