  We present a new rank-adaptive tensor method to compute the numerical
solution of high-dimensional nonlinear PDEs. The method combines functional
tensor train (FTT) series expansions, operator splitting time integration, and
a new rank-adaptive algorithm based on a thresholding criterion that limits the
component of the PDE velocity vector normal to the FTT tensor manifold. This
yields a scheme that can add or remove tensor modes adaptively from the PDE
solution as time integration proceeds. The new method is designed to improve
computational efficiency, accuracy and robustness in numerical integration of
high-dimensional problems. In particular, it overcomes well-known computational
challenges associated with dynamic tensor integration, including low-rank
modeling errors and the need to invert covariance matrices of tensor cores at
each time step. Numerical applications are presented and discussed for linear
and nonlinear advection problems in two dimensions, and for a four-dimensional
Fokker-Planck equation.
