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We demonstrate the utility of machine learning algorithms for the design of Oscillatory Neural Networks (ONNs). After constructing a circuit model of the oscillators in a machine-learning-enabled simulator and performing Backpropagation through time (BPTT) for determining the coupling resistances between the ring oscillators, we show the design of associative memories and multi-layered ONN classifiers. The machine-learning-designed ONNs show superior performance compared to other design methods (such as Hebbian learning) and they also enable significant simplifications in the circuit topology. We demonstrate the design of multi-layered ONNs that show superior performance compared to single-layer ones. We argue Machine learning can unlock the true computing potential of ONNs hardware.