Reduced order modelling using neural networks for predictive modelling of 3d-magneto-mechanical problems with application to magnetic resonance imaging scanners

The design of magnets for magnetic resonance imaging (MRI) scanners requires the numerical simulation of a coupled magneto-mechanical system where the effects that different material parameters and in-service loading conditions have on both imaging and MRI performance are key to aid with the design and the manufacturing process. To correctly capture the complex physics, and to obtain accurate solutions, finite element simulations with dense meshes and high order elements are needed. Reduced order model approaches, based on the established proper orthogonal decomposition (POD) approach, are attractive as they can rapidly predict the numerical simulations needed under changing parameters or conditions. However, the projected (PODP) approach has an invasive computational implementation, whilst the interpolated (PODI) approach presents challenges when the dimension of the space of parameters to be investigated becomes large. As an alternative, we investigate a POD technique based on using a neural network regression, which is not as invasive as PODP, but has superior approximation properties compared to PODI. We apply this to the coupled magneto-mechanical system to understand three pressing industrial problems: firstly, the accurate and rapid computation of the resonant frequencies associated with this coupled magneto-mechanical system, secondly, the effects of magnet motion on the Ohmic power and kinetic energy curves, and, thirdly, the prediction of the uncertainty in Ohmic power and kinetic energy curves as a function of exciting frequency for uncertain material parameters.