Time- and memory-efficient representation of complex mesoscale potentials

TL;DR

This paper introduces a tensor train cross approximation method to efficiently model complex mesoscale potentials, demonstrated on van der Waals interactions between cylindrical nanostructures, enabling faster and more memory-efficient simulations.

Contribution

It presents a novel application of tensor train decomposition for representing mesoscale potentials in nanomechanics, improving computational efficiency and universality.

Findings

Achieved compact tensor representations of interaction potentials.

Reduced computational time and memory usage.

Applicable to complex-shaped nanostructures in mesoscale modeling.

Abstract

We apply the modern technique of approximation of multivariate functions - tensor train cross approximation - to the problem of the description of physical interactions between complex-shaped bodies in a context of computational nanomechanics. In this note we showcase one particular example - van der Waals interactions between two cylindrical bodies - relevant to modeling of carbon nanotube systems. The potential is viewed as a tensor (multidimensional table) which is represented in compact form with the help of tensor train decomposition. The described approach offers a universal solution for the description of van der Waals interactions between complex-shaped nanostructures and can be used within the framework of such systems of mesoscale modeling as recently emerged mesoscopic distinct element method (MDEM).