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We present some results on stabilization for reduced-order models (ROMs) ofpartial differential equations. The stabilization is achieved using Lyapunovtheory to design a new closure model that is robust to parametricuncertainties. The free parameters in the proposed ROM stabilization method areoptimized using a model-free multi-parametric extremum seeking (MES) algorithm.The 3D Boussinesq equations provide a challenging numerical test-problem thatis used to demonstrate the advantages of the proposed method.

Robust Reduced-Order Model Stabilization for Partial Differential  Equations Based on Lyapunov Theory and Extremum Seeking with Application to  the 3D Boussinesq Equations