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Accurate modeling of the mean magnetic moment of an ensemble of magnetic particles in dynamic magnetic fields is a challenging task that requires sophisticated differential equation solvers. However, these methods are computationally costly and therefore not practical for long excitation sequences such as those of the Lissajous type. In this paper we propose to accelerate simulations by using a neural network mapping from the input parameter functions that are applied to the original particle simulator directly to the mean magnetic moment output function. The architecture of the neural network is based on the Fourier neural operator, which allows to train mappings between function spaces. Our results show that the particle simulation can be accelerated by a factor of about 200 while the relative error of the neural network simulator remains below 1.5%.