Time integration of tree tensor networks

Understand

Dynamical low-rank approximation by tree tensor networks is studied for the data-sparse approximation to large time-dependent data tensors and unknown solutions of tensor differential equations.

• A time integration method for tree tensor networks of prescribed tree rank is presented and analyzed.
• It extends the known projector-splitting integrators for dynamical low-rank approximation by matrices and Tucker tensors and is shown to inherit their favorable properties.
• The integrator is based on recursively applying the Tucker tensor integrator.