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Low-Rank Tensor Approximation for High-Order Correlation Functions of Gaussian Random Fields

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dc.contributor.author Kumar, Rajesh
dc.date.accessioned 2023-08-11T08:47:01Z
dc.date.available 2023-08-11T08:47:01Z
dc.date.issued 2015
dc.identifier.uri https://epubs.siam.org/doi/10.1137/140968938
dc.identifier.uri http://dspace.bits-pilani.ac.in:8080/xmlui/handle/123456789/11316
dc.description.abstract Gaussian random fields are widely used as building blocks for modeling stochastic processes. This paper is concerned with the efficient representation of d-point correlations for such fields, which in turn enables the representation of more general stochastic processes that can be expressed as a function of one (or several) Gaussian random fields. Our representation consists of two ingredients. In the first step, we replace the random field by a truncated Karhunen--Loève expansion and analyze the resulting error. The parameters describing the d-point correlation can be arranged in a tensor, but its storage grows exponentially in d. To avoid this, the second step consists of approximating the tensor in a low-rank tensor format, the so-called tensor train decomposition. By exploiting the particular structure of the tensor, an approximation algorithm is derived that does not need to form this tensor explicitly and allows processing correlations of order as high as d=20. The resulting representation is very compact, and its use is illustrated for elliptic partial differential equations with random Gaussian forcing terms. en_US
dc.language.iso en en_US
dc.publisher SIAM en_US
dc.subject Mathematics en_US
dc.subject Gaussian random fields en_US
dc.subject Low-rank approximation en_US
dc.subject Karhunen--Loève expansion en_US
dc.subject Tensor train decomposition en_US
dc.title Low-Rank Tensor Approximation for High-Order Correlation Functions of Gaussian Random Fields en_US
dc.type Article en_US


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