  Motivated by stability analysis of large scale power systems, we describe how
the Lasserre (moment-sums of squares, SOS) hierarchy can be used to generate
outer approximations of the region of attraction (ROA) of sparse polynomial
differential systems, at the price of solving linear matrix inequalities (LMI)
of increasing size. We identify specific sparsity structures for which we can
provide numerically certified outer approximations of the region of attraction
in high dimension. For this purpose, we combine previous results on non-sparse
ROA approximations with sparse semi-algebraic set volume computation.
