ISSN 2079-3537      

 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             

Scientific Visualization, 2022, volume 14, number 3, pages 73 - 91, DOI: 10.26583/sv.14.3.06

On the Visualization of Multidimensional Functions using Canonical Decomposition

Authors: A.K.  Alekseev1,,, A.E.  Bondarev 2,A, Yu.S.  Pyatakova3,B

A Keldysh Institute of Applied Mathematics RAS

B Korolev Rocket and Space Corporation Energia, Korolev, Russia

1 ORCID: 0000-0001-8317-8688, aleksey.k.alekseev@gmail.com

2 ORCID: 0000-0003-3681-5212, bond@keldysh.ru

3 ORCID: 0000-0002-8055-7807, yuliya.pyatakova@rsce.ru

 

Abstract

The approximation of a multidimensional function by means of tensor decompositions is considered in terms of storage, processing and visualization of the results of parametric calculations in computational aerogasdynamics problems. An algorithm for calculating the canonical decomposition using a combination of the alternative least squares method and stochastic gradient descent is described. Numerical results for interpolation of functions in six-dimensional space obtained using the canonical decomposition are presented, demonstrating the high computational efficiency and quality of results. Visual representations of the results are provided.

 

Keywords: tensor decomposition, canonical decomposition, computational fluid dynamics, visual representation of results.