Discussion of some simple examples of approximation spaces and linear or nonlinear, intrusive or non-intrusive reduced models
After a very brief introduction to reduced models, the presentation focuses on very simple examples of parametric problems
governed by partial differential equations in which the linear representation of the reduced space fails. We then discuss a technique for
of nonlinear approximation based on the mapping, as a function of the variation of the parameter, of the “features” of the solution via the optimal transport.
In this context, we conclude by discussing the advantages and disadvantages of an intrusive or non-intrusive approach and extensions of the method.
In collaboration with S. Cucchiara, T. Taddei, H. Telib
