Parametric model order reduction using tensor principal orthogonal decomposition

In this talk we will present tensor principal orthogonal decomposition (TPOD), a data-driven parametric model order reduction approach based on the multilinear singular value decomposition (MLSVD). Similarly to the principal orthogonal decomposition (POD), TPOD requires that a full order model be simulated with different parameter sample values. The obtained state trajectory snapshots are then organized in a snapshot tensor such that the state-space variables are arranged along the first and the simulation time steps along the second mode. Third and higher modes of the snapshot tensor represent the respective parameter sample values. This snapshot tensor is subsequently decomposed using the MLSVD into a core tensor and at least three factor matrices: A state-space basis factor matrix (cf. the left singular vectors of the matrix SVD), time coefficients factor matrix (cf. the right singular vectors of the matrix SVD), and parameter coefficients factor matrices. Now a reduced basis for an unsampled parameter value can be computed by interpolating the relevant rows of parameter coefficients factor matrices and recombining them with the core tensor. We show that this is equivalent to applying matrix SVD to appropriately interpolated state trajectory snapshots. However, due to the MLSVD decomposition step and the associated data compression, TPOD is much more time and memory efficient. To demonstrate the performance of TPOD, we apply it to community benchmarks with one and two parameters and discuss its approximation quality as well as its runtime and memory consumption.     «

In this talk we will present tensor principal orthogonal decomposition (TPOD), a data-driven parametric model order reduction approach based on the multilinear singular value decomposition (MLSVD). Similarly to the principal orthogonal decomposition (POD), TPOD requires that a full order model be simulated with different parameter sample values. The obtained state trajectory snapshots are then organized in a snapshot tensor such that the state-space variables are arranged along the first and...     »