Multifidelity Proper Orthogonal Decomposition
Karen Willcox
University of Texas at Austin
The proper orthogonal decomposition (POD) is widely used to compute a low-dimensional basis that underpins a subsequent dimension reduction or reduced-order modeling step. POD is data-driven in the sense that it requires a training data set of high-fidelity solutions, typically referred to as snapshots. For many complex scientific applications, the computational cost of generating these snapshots is prohibitive, especially when their generation requires sampling over a high-dimensional parameter space. This talk presents a multifidelity POD (mfPOD) formulation that leverages cheaper, lower-fidelity snapshots to reduce the computational cost of computing the POD basis. Our mfPOD method is built on the theory of control variates. Numerical results show that mfPOD achieves computational speedups that translate into useful gains in large-scale problems. Joint work with Nicole Aretz.