Physics-Informed Neural Networks for Solving Parametric Magnetostatic Problems

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 mini...

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Bibliographic Details
Published in:IEEE transactions on energy conversion 2022-12, Vol.37 (4), p.2678-2689
Main Authors: Beltran-Pulido, Andres, Bilionis, Ilias, Aliprantis, Dionysios
Format: Article
Language:English
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
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Summary: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.
ISSN:0885-8969
1558-0059
DOI:10.1109/TEC.2022.3180295