An oscillatory neural network (ONN) is a neuromorphic computing paradigm based on encoding of information into the phases of oscillators. In this paper we present an ONN whose elemental unit, the "neuron", is implemented through a beyond-CMOS device based on vanadium dioxide (VO 2 ). Such ONN technology provides ultra-low power solutions for performing pattern recognition tasks, and it is ideally suited for edge computing applications. However, exploring the groundwork of the beyond-CMOS ONN paradigm is mandatory premise for its industry-level exploitation. Such foundation entails the building of a holistic simulation flow from materials and devices to circuits, to allow assessment of ONN performance. In this work we report results of this advanced designing approach with special focus over the VO 2 oscillator. This establishes the ground to scale up to evaluate beyond-CMOS ONN functionalities for pattern recognition.