Physics-Informed Neural Networks for Solving Parametric Magnetostatic Problems

• Published in: IEEE transactions on energy conversion Vol. 37; no. 4; pp. 2678 - 2689
• Main Authors: Beltran-Pulido, Andres, Bilionis, Ilias, Aliprantis, Dionysios
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Artificial neural networks; Design parameters; Electromagnet; Electromagnets; energy functional; Finite element analysis; Finite element method; Geometric accuracy; Geometry; Magnetic domains; Magnetic fields; Magnetostatics; Neural networks; parametric magnetostatics; physics-informed neural networks; Stochastic processes; Windings
• ISSN: 0885-8969; 1558-0059
• DOI: 10.1109/TEC.2022.3180295

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.