Learning-based Reduced Order Model Stabilization for Partial Differential Equations: Application to the Coupled Burgers Equation

Mouhacine Benosman, Boris Kramer, Petros Boufounos, Piyush Grover

Abstract: We present results on stabilization for reduced order models (ROM) of partial differential equations using learning. Stabilization is achieved via closure models for ROMs, where we use a model-free extremum seeking (ES) dither-based algorithm to learn the best closure models' parameters, for optimal ROM stabilization. We first propose to auto-tune linear closure models using ES, and then extend the results to a closure model combining linear and nonlinear terms, for better stabilization performance. The coupled Burgers' equation is employed as a test-bed for the proposed tuning method.