Constitutive equations are used in electromagnetic field simulations to model a material response to applied fields or forces. The $B(H)$ characteristic of iron laminations depends on thermal and mechanical stresses that may have occurred during the manufacturing process. Data-driven modelling and updating of the $B(H)$ characteristic are therefore well known necessities. In this work the $B(H)$ curve of an iron yoke of an accelerator magnet is updated based on observed magnetic flux density data by solving a non-linear inverse problem. The inverse problem is regularized by restricting the solution to the function space that is spanned by the truncated Karhunen Loeve expansion of a stochastic $B(H)$-curve model based on material measurements. It is shown that this method is able to retrieve a previously selected ground truth $B(H)$-curve. With the update of the $B(H)$ characteristic, the numerical model gains predictive capacities for excitation currents that were not included in the data.

翻译：在电磁场仿真中，本构方程用于建模材料对外加场或力的响应。铁芯叠片的$B(H)$特性取决于制造过程中可能产生的热应力和机械应力。因此，数据驱动的$B(H)$特性建模与更新是公认的必要环节。本研究通过求解非线性逆问题，基于观测的磁通密度数据，更新了加速器磁体铁轭的$B(H)$曲线。该逆问题通过将解限制在由材料测量数据建立的随机$B(H)$曲线模型的截断Karhunen-Loève展开所张成的函数空间中进行正则化。结果表明，该方法能够恢复预先选定的真实$B(H)$曲线。通过更新$B(H)$特性，数值模型获得了对未包含在数据中的励磁电流的预测能力。