  For an isolated generic quantum system out of equilibrium, the long time
average of observables is given by the diagonal ensemble, i.e. the mixed state
with the same probability for energy eigenstates as the initial state but
without coherences between different energies. In this work we present a method
to approximate the diagonal ensemble using tensor networks. Instead of
simulating the real time evolution, we adapt a filtering scheme introduced
earlier in [Phys. Rev. B 101, 144305 (2020)] to this problem. We analyze the
performance of the method on a non-integrable spin chain, for which we observe
that local observables converge towards thermal values polynomially with the
inverse width of the filter.
