Maximum-entropy principle as Galerkin modelling paradigm

We show how the empirical Galerkin method, leading e.g. to POD models, can be derived from maximum-entropy principles building on Noack \& Niven 2012 JFM. In particular, principles are proposed (1) for the Galerkin expansion, (2) for the Galerkin system identification, and (3) for the probability distribution of the attractor. Examples will illustrate the advantages of the entropic modelling paradigm.