  This work presents a data-driven magnetostatic finite-element solver that is
specifically well-suited to cope with strongly nonlinear material responses.
The data-driven computing framework is essentially a multiobjective
optimization procedure matching the material operation points as closely as
possible to given material data while obeying Maxwell's equations. Here, the
framework is extended with heterogeneous (local) weighting factors - one per
finite element - equilibrating the goal function locally according to the
material behavior. This modification allows the data-driven solver to cope with
unbalanced measurement data sets, i.e. data sets suffering from unbalanced
space filling. This occurs particularly in the case of strongly nonlinear
materials, which constitute problematic cases that hinder the efficiency and
accuracy of standard data-driven solvers with a homogeneous (global) weighting
factor. The local weighting factors are embedded in the distance-minimizing
data-driven algorithm used for noiseless data, likewise for the maximum entropy
data-driven algorithm used for noisy data. Numerical experiments based on a
quadrupole magnet model with a soft magnetic material show that the proposed
modification results in major improvements in terms of solution accuracy and
solver efficiency. For the case of noiseless data, local weighting factors
improve the convergence of the data-driven solver by orders of magnitude. When
noisy data are considered, the convergence rate of the data-driven solver is
doubled.
