  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.
