Dynamical low-rank approximation is a rather new and important topic, which was studied by Lubich and Koch for low-rank matrices and low-rank (in the sense of Tucker format) tensor decomposition. Such kind of techniques were well known in physics in chemistry, going back to Dirac-Frenkel principle, and MCTDH method for the computation of quantum molecular vibrations. It was interesting to extend this approach to the TT-format.
We did it in our recent paper**Efficient time-stepping scheme for dynamics on TT-manifolds**, which is published as a preprint in MIS MPI Leipzig. In fact, we managed to provide an efficient numerical scheme for the computation of the TT-dynamics. The MATLAB implementation will be soon included in the development github repository of the TT-Toolbox.