@Article{CiCP-16-1,
author = {},
title = {Approximation of Spatio-Temporal Random Processes Using Tensor Decomposition},
journal = {Communications in Computational Physics},
year = {2014},
volume = {16},
number = {1},
pages = {75--95},
abstract = {<p style="text-align: justify;">A new representation of spatio-temporal random processes is proposed in
this work. In practical applications, such processes are used to model velocity fields,
temperature distributions, response of vibrating systems, to name a few. Finding an
efficient representation for any random process leads to encapsulation of information
which makes it more convenient for a practical implementations, for instance, in a
computational mechanics problem. For a single-parameter process such as spatial or
temporal process, the eigenvalue decomposition of the covariance matrix leads to the
well-known Karhunen-Loève (KL) decomposition. However, for multiparameter processes such as a spatio-temporal process, the covariance function itself can be defined
in multiple ways. Here the process is assumed to be measured at a finite set of spatial
locations and a finite number of time instants. Then the spatial covariance matrices at
different time instants are considered to define the covariance of the process. This set
of square, symmetric, positive semi-definite matrices is then represented as a third-order tensor. A suitable decomposition of this tensor can identify the dominant components of the process, and these components are then used to define a closed-form
representation of the process. The procedure is analogous to the KL decomposition for
a single-parameter process, however, the decompositions and interpretations vary significantly. The tensor decompositions are successfully applied to (i) a heat conduction
problem, (ii) a vibration problem, and (iii) a covariance function taken from the literature that was fitted to model a measured wind velocity data. It is observed that the
proposed representation provides an efficient approximation to some processes. Furthermore, a comparison with KL decomposition showed that the proposed method is
computationally cheaper than the KL, both in terms of computer memory and execution time.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.201112.191113a},
url = {https://global-sci.com/article/80430/approximation-of-spatio-temporal-random-processes-using-tensor-decomposition}
}