Collocation Model Order Reduction: Application to Nonlinear Approximation Manifold
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In this work, we introduce a novel reduced-order strategy, termed collocation Model Order Reduction (cMOR), as an alternative to projection-based Model Order Reduction (pMOR). Unlike pMOR, which relies on projection to obtain the reduced solution, cMOR determines the solution at specific collocation points selected via hyper-reduction techniques. The method retains the two-phase structure of pMOR, comprising an offline learning phase, where a Reduced Basis (RB) is built from snapshots, and an online phase, where the High-Dimensional Model (HDM) is evaluated locally over the empirical subset of points before reconstructing the full solution through the RB. We apply cMOR within the framework of nonlinear approximation manifolds (NAM), which generalize the concept of reduced spaces by embedding the solution onto a nonlinear manifold rather than a linear subspace. This approach enhances the ability to capture complex, multiscale phenomena in fluid dynamics while preserving the simplicity and non-intrusive nature of cMOR, facilitating its integration into existing computational frameworks.