Karhunen-Loéve Decomposition of Isotropic Gaussian Random Fields Using a Tensor Approximation of Autocovariance Kernel

0495896 - ÚGN 2019 RIV CH eng C - Konferenční příspěvek (zahraniční konf.)
Béreš, Michal
Karhunen-Loéve Decomposition of Isotropic Gaussian Random Fields Using a Tensor Approximation of Autocovariance Kernel.
High Performance Computing in Science and Engineering. HPCSE 2017. Cham: Springer, 2018 - (Kozubek, T.), s. 188-202. Lecture Notes in Computer Science, Code 216349, Volume 11087. ISBN 978-3-319-97135-3.
[HPCSE 2017: International Conference on High Performance Computing in Science and Engineering /3./. Karolinka (CZ), 22.05.2017-25.05.2017]
Grant CEP: GA MŠMT LQ1602; GA MŠMT LD15105
Institucionální podpora: RVO:68145535
Klíčová slova: random fields sampling * Karhunen-Loève decomposition * tensor approximation * numerical integration
Obor OECD: Applied mathematics
https://link.springer.com/content/pdf/10.1007%2F978-3-319-97136-0_14.pdf

Applications of random fields typically require a generation of random samples or their decomposition. In this contribution, we focus on the decomposition of the isotropic Gaussian random fields on a two or three-dimensional domain. The preferred tool for the decomposition of the random field is the Karhunen-Loéve expansion. The Karhunen-Loéve expansion can be approximated using the Galerkin method, where we encounter two main problems. First, the calculation of each element of the Galerkin matrix is expensive because it requires an accurate evaluation of multi-dimensional integral. The second problem consists of the memory requirements, originating from the density of the matrix. We propose a method that overcomes both problems. We use a tensor-structured approximation of the autocovariance kernel, which allows its separable representation. This leads to the representation of the matrix as a sum of Kronecker products of matrices related to the one-dimensional problem, which significantly reduces the storage requirements. Moreover, this representation dramatically reduces the computation cost, as we only calculate two-dimensional integrals.
Trvalý link: http://hdl.handle.net/11104/0288771