This work presents a reduced order modelling framework based on unsupervised and supervised learning for inferring the torque of a permanent magnet synchronous machine for different design configurations. Given a dataset of torque-versus-rotation-angle samples, each corresponding to a different set of design parameters, the torque's dimension is first reduced to its main components. Dimension reduction is performed in an unsupervised learning manner by post-processing the results of a discrete Fourier transform applied to the torque samples. This allows us to take advantage of torque periodicity and preserve frequency-related physical information in the reduced components. Next, a surrogate model mapping the machine's design parameters to the reduced torque components is computed by means of supervised learning, where the trained models are polynomial chaos expansions, artificial neural networks, or Gaussian processes. Torque inference is performed by evaluating the surrogate model for new design parameter values, followed by inverting the dimension reduction. The complete framework is used for uncertainty quantification in electric machine design with random geometrical variations. Numerical results show that the proposed framework leads to sufficiently accurate torque estimates for previously unseen design configurations. Fourier transform-based dimension reduction is found to be significantly advantageous compared to surrogate modelling the original (not reduced) torque signal, as well as slightly advantageous compared to dimension reduction via the standard method of principal component analysis, irrespective of surrogate model choice. The combination of Fourier transform-based dimension reduction with Gaussian process-based surrogate modelling is found to be the best-in-class approach for this use case. Last, the surrogate-based uncertainty estimates are almost indistinguishable to Monte Carlo reference results, however, the former are computed at much reduced computational cost.