Data?driven solvers for strongly nonlinear material response

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