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Using machine learning, we explore the utility of various deep neural networks (NN) when applied to high harmonic generation (HHG) scenarios. First, we train the NNs to predict the time-dependent dipole and spectra of HHG emission from reduced-dimensionality models of di- and triatomic systems based of on sets of randomly generated parameters (laser pulse intensity, internuclear distance, and molecular orientation). These networks, once trained, are useful tools to rapidly generate the HHG spectra of our systems. Similarly, we have trained the NNs to solve the inverse problem - to determine the molecular parameters based on HHG spectra or dipole acceleration data. These types of networks could then be used as spectroscopic tools to invert HHG spectra in order to recover the underlying physical parameters of a system. Next, we demonstrate that transfer learning can be applied to our networks to expand the range of applicability of the networks with only a small number of new test cases added to our training sets. Finally, we demonstrate NNs that can be used to classify molecules by type: di- or triatomic, symmetric or asymmetric, wherein we can even rely on fairly simple fully connected neural networks. With outlooks toward training with experimental data, these NN topologies offer a novel set of spectroscopic tools that could be incorporated into HHG experiments.