On identification of self-similar characteristics using the Tensor Train decomposition method with application to channel turbulence flow

TL;DR

This paper explores the use of Tensor Train decomposition to efficiently analyze 3D turbulence flow data, demonstrating high compression and accurate pattern capture in complex fluid dynamics simulations.

Contribution

It introduces the application of Tensor Train decomposition to channel turbulence data, highlighting its effectiveness in data compression and pattern recognition.

Findings

Tensor Train captures self-similar patterns effectively

High compression rates achieved with low errors

Shape of input tensor influences compression efficiency

Abstract

A study on the application of the Tensor Train decomposition method to 3D direct numerical simulation data of channel turbulence flow is presented. The approach is validated with respect to compression rate and storage requirement. In tests with synthetic data, it is found that grid-aligned self-similar patterns are well captured, and also the application to non grid-aligned self-similarity yields satisfying results. It is observed that the shape of the input Tensor significantly affects the compression rate. Applied to data of channel turbulent flow, the Tensor Train format allows for surprisingly high compression rates whilst ensuring low relative errors.