  In this work we present recent results on application of low-rank tensor
decompositions to modelling of aggregation kinetics taking into account
multi-particle collisions (for three and more particles). Such kinetics can be
described by system of nonlinear differential equations with right-hand side
requiring $N^D$ operations for its straight-forward evaluation, where $N$ is
number of particles size classes and $D$ is number of particles colliding
simultaneously. Such a complexity can be significantly reduced by application
low rank tensor decompositions (either Tensor Train or Canonical Polyadic) to
acceleration of evaluation of sums and convolutions from right-hand side.
Basing on this drastic reduction of complexity for evaluation of right-hand
side we further utilize standard second order Runge-Kutta time integration
scheme and demonstrate that our approach allows to obtain numerical solutions
of studied equations with very high accuracy in modest times. We also show
preliminary results on parallel scalability of novel approach and conclude that
it can be efficiently utilized with use of supercomputers.
