Optimal Multi-Physics Synthesis of a Dual-Frequency Power Inductor Using Deep Neural Networks and Gaussian Process Regression

In this paper, a multi-physics case study belonging to the class of induction heating problem is considered. Finite Element Analysis is used to evaluate the temperature along a line on a graphite disk heated by two power inductors. In order to build a surrogate field model of the device, i.e., to compute the temperature profile on the disk, given the amplitudes and frequencies of the supply currents, three methods have been used (Support Vector Regression (SVR), fully connected Neural Network (NN) and Gaussian Process Regression (GPR)). In turn, to solve the inverse problem, i.e., to identify frequencies and currents of the two coils, given a prescribed temperature profile, two approaches have been implemented. The former is an optimization approach based on a multi-objective formulation, solved by means of the NSGA-II algorithm; the latter is a two-step procedure, based on fully connected Deep Neural Networks (DNNs), solving an optimal design problem first and, subsequently, an optimal control problem.