Speaker
Description
spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced and full-order non-intrusive modeling, namely Operator Inference (OpInf) and sparse Full-Order Model (sFOM) inference. We decompose the domain into two complementary subdomains which exhibit fast and slow singular value decay, accordingly. The dynamics on the subdomain exhibiting slow singular value decay are learned using sFOM while the
dynamics with intrinsically low dimensionality on the complementary subdomain are learned using OpInf. The resulting, coupled OpInf-sFOM formulation leverages the computational efficiency of OpInf and the high spatial resolution of sFOM and thus enables fast non-intrusive predictions for localized features with slow singular value decay, such as transport-dominated dynamics. Furthermore, we propose a novel, stability-promoting regularization technique with a closed-form solution based on the Gershgorin disk theorem for both sFOM and OpInf models and evaluate the efficiency of the coupled approach in terms of offline and online speedup. Finally, we demonstrate the capabilities of the coupled OpInf-sFOM formulation for testcases such as the one-dimensional, viscous Burgers’ equation and a two-dimensional parametric model for the Pine Island Glacier ice thickness dynamics.
