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We consider the low-rank tensor train completion problem when additional sideinformation is available in the form of subspaces that contain the mode-$k$fiber spans. We propose an algorithm based on Riemannian optimization to solvethe problem. Numerical experiments show that the proposed algorithm requiresfar fewer known entries to recover the tensor compared to standard tensor traincompletion methods.

Note: low-rank tensor train completion with side information based on Riemannian optimization