The Q and U Bolometric Interferometer for Cosmology (QUBIC) is a ground-based telescope which will observe the cosmic microwave background (CMB) with the goal of detecting its extremely faint primordial B-mode polarization pattern as observational evidence for the theory of inflation in the early Universe. QUBIC has a novel bolometric interferometer design that allows it to have precise control over instrument systematics and to remove astronomical foregrounds which would otherwise obscure the CMB polarization signal. Due to its interferometric design, QUBIC has a complex multi-peaked antenna beam pattern known as the synthesized beam which must be well known in order to correctly process the QUBIC data. We have modelled the QUBIC beam pattern at multiple frequencies and for detectors located at different positions in the focal plane using precise electromagnetic and physical optics simulations. For the complex setup of the QUBIC telescope these simulations are computationally expensive. In this work we use machine learning to interpolate the beam at multiple frequencies and detector locations in order to reduce the amount of computation required to model it. For our purposes, two types of neural networks were used: a Multilayer Perceptron (MLP) model and a Long Short-Term Memory (LSTM) model. For the amount of data generated, only the LSTM model was successful in replicating the synthesized beam to a satisfactory degree. We used the LSTM machine learning (ML) model to generate the synthesized beam for all 248 detectors at 150 GHz and compared its use in our analysis pipeline to a fully simulated PO beam and an approximate analytical model. From this it can be seen that although the ML prediction did not replicate the PO synthesized beam perfectly, it was closer than the beam produced with the analytical formula. Finally, we show the effect of the differences in beam pattern prediction on the recovered B-mode spectrum of the CMB.