Quantum mechanics

Function (biology)

Context (archaeology)

Algorithm

Magnetic field

Pure mathematics

Biology

Statistics

Applied mathematics

Field (mathematics)

Gradient descent

Computer science

Mathematical optimization

Evolutionary biology

Paleontology

Thermodynamics

Physics

Finite element method

Parameterized complexity

Stochastic gradient descent

Mathematics

Electromagnet

Minification

Artificial intelligence

Parametric statistics

Artificial neural network

Magnet

IEEE Transactions on Energy Conversion

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.

Physics-Informed Neural Networks for Solving Parametric Magnetostatic Problems