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\begin{document}

\title{Hierarchical Physics-Informed Neural Network Framework for 3D Magnetic
Modeling of Medium Frequency Transformers}



\author[1]{Xiao Yang}%
\author[1]{Liangcai Shu}%
\author[1]{Dongsheng Yang}%
\affil[1]{Affiliation not available}%


\vspace{-1em}



  
  \date{June 13, 2024}


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\begin{abstract}
Neural Network (NN) technology is revolutionizing the modeling paradigm
in the engineering arena, enhancing simultaneously model precision and
process speed. Nevertheless, the deficiency of physical interpretability
in current NN models causes an unattainable demand for the quantity of
training data, especially when dealing with high-dimension physical
behaviours. In this work, a Hierarchical Physics-Informed Neural Network
(HPINN) framework is proposed to address the 3D magnetic modeling issue
of Medium Frequency Transformers (MFTs). By establishing the knowledge
transfer channel between the cross section and the equivalent space, the
inferior 2D model parameter search space, which is restricted by
Dowell's equation and accessible 2D magnetic data information, can be
mapped into the superior 3D search space. Accordingly, with limited 3D
training data, the performance of the HPINN framework is still
guaranteed around the optimal state. The structural embedding of physics
knowledge reduces the model's reliance on 3D training data, thereby
relieving the strict computing requirement at the data generation stage.
Finally, according to the training results and experiment verifications,
with only one-third computational burden used in the classic NN model,
the average error of this proposed HPINN framework is reduced to 1\%,
and the maximum error does not exceed 10\%.%
\end{abstract}%



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