Learn Reduced Order Models in high-dimensional spaces.
Model reduction is known very challenging for high-dimensional parametric problems whose solutions also live in high-dimensional manifolds. However, often the manifold of some quantity of interest (QoI) depending on the parametric solutions is low-dimensional. LearnROM implements structure-exploiting algorithms to efficiently learn the intrinsic parameter subspace in which the QoI is most sensitive. Both the gradient-based active subspace and Hessian-based subspace are implemented in LearnROM. Samples are drawn from such subspaces to learn the QoI-oriented ROM, which are demonstrated to be more efficient than the samples drawn randomly. See more details in the paper
@article{chen2019hessian,
title={Hessian-based sampling for high-dimensional model reduction},
author={Chen, Peng and Ghattas, Omar},
journal={International Journal for Uncertainty Quantification},
volume={9},
number={2},
year={2019},
publisher={Begel House Inc.}
}
