  We show that we can retrieve a Yang--Mills potential and a Higgs field (up to
gauge) from source-to-solution type data associated with the classical
Yang--Mills--Higgs equations in Minkowski space $\mathbb{R}^{1+3}$. We impose
natural non-degeneracy conditions on the representation for the Higgs field and
on the Lie algebra of the structure group which are satisfied for the case of
the Standard Model. Our approach exploits the non-linear interaction of waves
generated by sources with values in the centre of the Lie algebra showing that
abelian components can be used effectively to recover the Higgs field.
