Structured Neural Network Models for Anisotropic Magnetic Constitutive Laws
Abstract
High-performance electrical steel used for iron cores of power transformers and generators exhibits complex material behavior. While modeling and simulation of isotropic nonlinear response is well understood, the incorporation of magnetic anisotropy remains challenging. This work proposes to utilize a structured neural network architecture to systematically describe the anisotropic nonlinear anhysteretic magnetic material response of electrical steel sheets. By constructing a convex and smooth co-energy density with dedicated behavior at infinity, we can ensure thermodynamic consistency and correct physical behavior and further guarantee basic mathematical properties which provide well-posedness of corresponding magnetic field problems and efficient numerical solvers. Numerical tests demonstrate the capability of the proposed method to describe strongly anisotropic behavior as well as its robust convergence in finite-element simulations.
Related
- Concurrent enforcement of polyconvexity and true-stress-true-strain monotonicity in incompressible isotropic hyperelasticity: application to neural network constitutive models
- Well-posed by Design: Learning Constitutive Laws from Velocity Data using Convex Neural Network Potentials
- An Adaptive Transferable Neural Network for Partial Differential Equations with Anisotropic or Sharp Solutions
- Polyconvex neural-network surrogates with learned paired directional features for anisotropic hyperelastic homogenization
- Neural Constitutive Learning for Generalized Reaction-Diffusion Systems
BibTeX
@misc{zeilinger2026structured,
title = {{Structured Neural Network Models for Anisotropic Magnetic Constitutive Laws}},
author = {Dorian Zeilinger and Felix Engertsberger and Herbert Egger},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03475},
eprint = {2611.03475},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03475},
}
RIS
TY - UNPB
TI - Structured Neural Network Models for Anisotropic Magnetic Constitutive Laws
AU - Dorian Zeilinger
AU - Felix Engertsberger
AU - Herbert Egger
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03475
UR - https://arxiv.org/abs/2611.03475
AB - High-performance electrical steel used for iron cores of power transformers and generators exhibits complex material behavior. While modeling and simulation of isotropic nonlinear response is well understood, the incorporation of magnetic anisotropy remains challenging. This work proposes to utilize a structured neural network architecture to systematically describe the anisotropic nonlinear anhysteretic magnetic material response of electrical steel sheets. By constructing a convex and smooth co-energy density with dedicated behavior at infinity, we can ensure thermodynamic consistency and correct physical behavior and further guarantee basic mathematical properties which provide well-posedness of corresponding magnetic field problems and efficient numerical solvers. Numerical tests demonstrate the capability of the proposed method to describe strongly anisotropic behavior as well as its robust convergence in finite-element simulations.
ER -