Table 1 Three examples of hybrid modeling

2

3D magnetostatics: BEM discretization

Fields measured by Hall probe or moving coil

Synthesis of physics and data by Bayesian update

3

2D/3D magnetostatics: Ampère’s & Gauss’s law

Measured material data points \((\boldsymbol{B}^{*}_{i},\boldsymbol{H}^{*}_{i} )\)

Projection of data into admissible physics manifold

4

Electromagnetic Darwin model

Data sampling from physics model

Bayesian Optimization: GP machine learning