  We introduce a new tensor integration method for time-dependent PDEs that
controls the tensor rank of the PDE solution via time-dependent diffeomorphic
coordinate transformations. Such coordinate transformations are generated by
minimizing the normal component of the PDE operator relative to the tensor
manifold that approximates the PDE solution via a convex functional. The
proposed method significantly improves upon and may be used in conjunction with
the coordinate-adaptive algorithm we recently proposed in JCP (2023) Vol. 491,
112378, which is based on non-convex relaxations of the rank minimization
problem and Riemannian optimization. Numerical applications demonstrating the
effectiveness of the proposed coordinate-adaptive tensor integration method are
presented and discussed for prototype Liouville and Fokker-Planck equations.
