Abstract
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 dataset 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. MFPOD then weights high- and low-fidelity snapshot data via a control-variate formulation to guarantee an unbiased estimate of the expected high-fidelity least-squares projection error. For constrained computational budgets, the mfPOD cost function has (under certain assumptions) lower variance than the POD cost function, which makes the mfPOD subspace more robust against variations in the training data and thus less prone to overfitting. Numerical results show that mfPOD achieves a one-order-of-magnitude improvement in computational speed, translating into significant gains for large-scale problems. Joint work with Nicole Aretz.
