IST Lunch Bunch
Intrinsic Sparse Mode Decomposition of High Dimensional Random Fields with Application to Stochastic Elliptic PDEs
Inspired by the recent developments in data sciences, we introduce an intrinsic sparse mode decomposition method for high dimensional random fields. This sparse representation of the random field allows us to break a high dimensional stochastic field into many spatially localized modes with low stochastic dimension locally. Such decomposition enables us to break the curse of dimensionality in the local PDE solvers. To obtain such representation, we first decompose the covariance function into low part plus sparse parts. We then extract the spatially localized modes from the sparse part by minimizing a surrogate of the total area of the support. Moreover, we provide an efficient algorithm to solve it. Upon such local representation, the computation for the elliptic PDEs with random media having high stochastic dimension is much easier. Various combinations of local and global solver achieve different levels of accuracy and efficiency. At the end of the talk, I will also discuss other applications of the intrinsic sparse mode extraction. This work is in collaboration with Thomas Y. Hou and Pengchuan Zhang.
Contact: Christine Ortega at 626.395.2076 email@example.com