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In this paper, we develop a predictive geometry control framework for jet-based additive manufacturing (AM) based on a physics-guided recurrent neural network (RNN) model. Because of its physically interpretable architecture, the model's parameters are obtained by training the network through back propagation using input-output data from a small number of layers. Moreover, we demonstrate that the model can be dually expressed such that the layer droplet input pattern for (each layer of) the part to be fabricated now becomes the network parameter to be learned by back-propagation. This approach is applied for feedforward predictive control in which the network parameters are learned offline from previous data and the control input pattern for all layers to be printed is synthesized. Sufficient conditions for the predictive controller's stability are then shown. Furthermore, we design an algorithm for efficiently implementing feedback predictive control in which the network parameters and input patterns (for the receding horizon) are learned online with no added lead time for computation. The feedforward control scheme is shown experimentally to improve the RMS reference tracking error by more than 30% over the state of the art. We also experimentally demonstrate that process uncertainties are compensated by the online learning and feedback control.