Nonlinear methods for model reduction

Typical model reduction methods for parametric partial differential equations construct a linear space V n which approximates well the solution manifold M consisting of all solutions u ( y ) with vector parameters. In many problems numerical computation, nonlinear such as adaptive approximation, -term and certain tree-based may provide improved efficiency over methods. Nonlinear replace by Σ . Little is known in terms their performance guarantees, most existing experiments use parameter dimension at two. this work, we make step towards more cohesive theory reduction. Framing these general setting library give first comparison standard approximation any compact set. We then study manifolds parametrized elliptic PDEs. specific example where domain split into finite number N rectangular cells, affine spaces m assigned to each cell, guarantees respect accuracy versus