  This paper developes a data-driven magnetostatic finite-element (FE) solver
which directly exploits measured material data instead of a material curve
constructed from it. The distances between the field solution and the
measurement points are minimized while enforcing Maxwell's equations. The
minimization problem is solved by employing the Lagrange multiplier approach.
The procedure wraps the FE method within an outer data-driven iteration. The
method is capable of considering anisotropic materials and is adapted to deal
with models featuring a combination of exact material knowledge and measured
material data. Thereto, three approaches with an increasing level of
intrusivity according to the FE formulation are proposed. The numerical results
for a quadrupole-magnet model show that data-driven field simulation is
feasible and affordable and overcomes the need of modeling the material law.
