Time Integration of Tree Tensor Networks

Dynamical low-rank approximation by tree tensor networks is studied for the data-sparse of large time-dependent data tensors and unknown solutions to differential equations. A time integration method prescribed rank presented analyzed. It extends known projector-splitting integrators dynamical matrices rank-constrained Tucker shown inherit their favorable properties. The integrator based on recursively applying integrator. In every step, climbs up down tree: it uses a recursion that passes from root leaves construction initial value problems subtree using appropriate restrictions prolongations, another update factors in network. reproduces given specified exactly robust typical presence small singular values matricizations connection tensors, contrast standard applied equations networks.