Intrusive and Non-Intrusive Reduced Models Based on Convex Displacement Interpolation
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The presentation focuses on examples of parametric problems governed by partial differential equations in which the linear representation of the reduced space fails. We introduce a nonlinear approximation technique called convex displacement interpolation based on a solution mapping based on optimal transportation. We discuss the advantages and disadvantages in this framework of linear or nonlinear, intrusive or non-intrusive model reduction approaches.