Physics-Informed Neural Networks for Inverse Electromagnetic Problems

Physics-informed neural networks (PINNs) have been successfully applied in electromagnetism (EM) for the solution of direct problems. However, since PINNs typically do not take system parameters (like geometry or material properties) as input, when embedded in inverse problems or adopted for parametrical studies, to output the solution of the governing equations, they require additional training for each new system parameter set. To overcome this issue, we propose a hypernetwork (HNN) that receives system parameters and outputs the network weights of a PINN, which in turn provides the solution of the direct problem. Therefore, once trained, the HNN acts as a parametrized real-time field solver that allows the fast solution of inverse problems, in which the objective(s) are defined a posteriori (i.e., after HNN's training). This method is adopted for a coil optimal design task in magnetostatics.