Real-time prediction by data-driven models applied to induction heating process

Data-driven modeling approach constitutes an appealing alternative to the finite element method for optimizing complex multiphysics parametrized problems. In this context, this paper aims at proposing a parametric solution for the temperature-time evolution during the multiphysics induction heating process by using a data-driven non-intrusive modeling approach. To achieve this goal, firstly, a set of synthetic solutions was collected, at some sparse sensors in the space domain and for properly selected process parameters, by solving the full-order finite element models using FORGE® software. Then, the gappy proper orthogonal decomposition method was used to complete the missing data. Next, the proper orthogonal decomposition method coupled with the nonlinear sparse proper generalized decomposition regression method was applied to find a low-dimensional space onto which the original solutions were projected and a model for the low-dimensional representations was, therefore, created. Hence, a real-time prediction of the temperature-time evolution and for any new process parameters could be efficiently computed at the predefined positions (sensors) in the space domain. Finally, spatial interpolation was carried out to extend the solutions everywhere in the spatial domain by applying a strategy based on the nonlinear dimensionality reduction by locally linear embedding method and the proper orthogonal decomposition method with radial basis functions interpolation. It was shown that the results are promising and the applied approaches provide good approximations in the low-data limit case.