  We report on our ongoing computation of the perturbative running of the
Yang-Mills coupling using gradient flow techniques. In particular, we use the
gradient flow method with twisted boundary conditions to perform a perturbative
expansion of the expectation value of the Yang-Mills energy density up to
fourth order in the coupling at finite flow time. We regularise the resulting
integrals using dimensional regularisation, and reproduce the universal
coefficient of the 1/{\epsilon} term in the relation between bare and
renormalised couplings. The computation of the finite part leading to a
determination of the {\Lambda} parameter in this scheme is underway.
