The increasing resource demands of artificial neural networks have prompted the exploration of novel platforms better suited for machine learning. In this context, phase oscillators represent a promising candidate due to their intrinsic nonlinearity and their ability to exhibit collective synchronization when coupled together. In the present work, we investigate one such implementation: a network of optomechanical oscillators pumped in the blue-detuned regime to achieve self-sustained oscillations. We propose a theoretical framework to describe their dynamics and demonstrate how such systems can be employed for neuromorphic computing. We discuss how they can be trained and analyze a platform, based on drum resonators, that could enable their physical implementation. Ultimately, the theoretical results obtained from modelling an XOR gate using 5 nodes in an all-to-all configuration are discussed.