  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
\mbox{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.
