This paper presents machine learning based approximations for the minimum number of driver nodes needed for structural controllability of networks under link-based random and targeted attacks. We compare our approximations with existing analytical approximations and show that our machine learning based approximations significantly outperform the existing closed-form analytical approximations in case of both synthetic and real-world networks. Apart from targeted attacks based upon the removal of so-called critical links, we also propose analytical approximations for out-in degree-based attacks.