Manifold construction and parameterization for nonlinear manifold-based model reduction

We present a new manifold construction and parameterization algorithm for model reduction approaches based on projection on manifolds. The new algorithm employs two key ideas: (1) we define an ideal manifold for nonlinear model reduction to be the solution of a set of differential equations with the property that the tangent space at any point on the manifold spans the same subspace as the low-order subspace (e.g., Krylov subspace generated by moment-matching techniques) of the linearized system; (2) we propose the concept of normalized integral curve equations, which are repeatedly solved to identify an almost-ideal manifold.