Tensor train optimization for the source problem of the partial differential equation using high performance computing Текст научной статьи по специальности «Компьютерные и информационные науки»

Inverse problems

Tensor

train

optimization

for

the

source

problem

of

the

partial

differential

equation

using

high

performance

computing

T. A. Zvonareva1,2, O. I. Krivorotko1,2

1Institute of Computational Mathematics and Mathematical Geophysics of SB RAS

2Novosibirsk State University

Email: t.zvonareva@g.nsu.ru

DOI 10.24412/cl‐35065‐2021‐1‐02‐20

The source problem for the diffusion‐logistic model based on a nonlinear partial differential equation,

which describes the process of information dissemination in social networks [1], is considered. The problem of

recovering a source from additional data about process in fixed time points is reduced to the problem of minimizing

the misfit function. The function is reduced to tensor form and minimization problem is formulate as a

problem of searching the minimal element in considering tensor. The optimization problem is solved by a

global method based on the expansion of the large dimension tensor in the tensor train format [2]. The program

code is spread across 48 CPUs.

This work is supported by the Council for Grants of the President of the Russian Federation (project no.

MK‐4994.2021.1.1).

References

1. Wang H., Wang F., Xu K. Modeling information diffusion in online social networks with partial differential

equations // arXiv: 1310.0505. 2013.

2. Oseledets I.V. Tensor‐train decomposition // SIAM J. Sci. Comput. 2011. V. 33, N. 5. P. 2295‐2317.