  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).
