Robust Adaptive Dynamic Mode Decomposition for Reduce Order Modelling of Partial Differential Equations

This work focuses on the design of stable reduced-order models (ROMs) for partial differential equations (PDEs) with parametric uncertainties. More specifically, we focus here on using dynamic mode decomposition (DMD) to reduce a PDE to a DMD-ROM and then pose the ROM stabilization or closure problem in the framework of nonlinear robust control. Using this robust control framework, we design two DMD-ROM closure models that are robust to parametric uncertainties and truncation of modes. We finally add an adaptation layer to our framework, where we tune the closure models in real-time, using data-driven extremum seeking controllers.