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We propose a guaranteed and fully computable upper bound on the energy normof the error in low-rank Tensor Train (TT) approximate solutions of (possibly)high dimensional reaction-diffusion problems. The error bound is obtained fromEuler-Lagrange equations for a complementary flux reconstruction problem, whichare solved in the low-rank TT representation using the block Alternating LinearScheme. This bound is guaranteed to be above the energy norm of the totalerror, including the discretization error, the tensor approximation error, andthe error in the solver of linear algebraic equations, although quadratureerrors, in general, can pollute its evaluation. Numerical examples with thePoisson equation and the Schroedinger equation with the Henon-Heiles potentialin up to 40 dimensions are presented to illustrate the efficiency of thisapproach.

Guaranteed a posteriori error bounds for low rank tensor approximate solutions