Physics-Informed Neural Networks for Solving Parametric Magnetostatic Problems
Andrés Beltrán-Pulido, Ilias Bilionis, Dionysios Aliprantis
Abstract
The objective of this paper is to investigate the ability of physics-informed neural networks to learn the magnetic field response as a function of design parameters in the context of a two-dimensional (2-D) magnetostatic problem. Our approach is as follows. First, we present a functional whose minimization is equivalent to solving parametric magnetostatic problems. Subsequently, we use a deep neural network (DNN) to represent the magnetic field as a function of space and parameters that describe geometric features and operating points. We train the DNN by minimizing the physics-informed functional using stochastic gradient descent. Lastly, we demonstrate our approach on a ten-dimensional EI-core electromagnet problem with parameterized geometry. We evaluate the accuracy of the DNN by comparing its predictions to those of finite element analysis.