When approximating a function that depend on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters prove ineffective. This is particularly true for responses from hyperbolic partial differential equations (PDEs) where linear low-dimensional bases are difficult to discover. We propose the use of displacement interpolation where the interpolation is done on the Lagrangian action of the optimal transport map between the function at nearby parameters, which allows an effective dimensionality reduction of hyperbolic phenomena. 查看全文>>