Neutrino astronomy is expanding into the ultra-high energy (>1017eV) frontier with the use of in-ice detection of Askaryan radio emission from neutrino-induced particle showers. There are already pilot arrays for validating the technology and the next few years will see the planning and construction of IceCube-Gen2, an upgrade to the current neutrino telescope IceCube. This thesis aims to facilitate that planning by providing faster simulations using deep learning surrogate models. Faster simulations could enable proper optimisation of the antenna stations providing better sensitivity and reconstruction of neutrino properties. The surrogates are made for two parts of the end-to-end simulations: the signal generation and the signal propagation. These two steps are the most time-consuming parts of the simulations. The signal propagation is modelled with a standard fully connected neural network whereas for the signal generation a conditional Wasserstein generative adversarial network is used. There are multiple reasons for using these types of models. For both problems the neural networks provide the speed necessary as well as being differentiable -both important factors for optimisation. Generative adversarial networks are used in the signal generation because of the inherent stochasticity in the particle shower development that leads to the Askaryan radio signal. A more standard neural network is used for the signal propagation as it is a regression task. Promising results are obtained for both tasks. The signal propagation surrogate model can predict the parameters of interest at the desired accuracy, except for the travel time which needs further optimisation to reduce the uncertainty from 0.5 ns to 0.1 ns. The signal generation surrogate model predicts the Askaryan emission well for the limited parameter space of hadronic showers and within 5° of the Cherenkov cone. The two models provide a first step and a proof of concept. It is believed that the models can reach the required accuracies with more work.