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This work presents a deep learning-based framework for the solution ofpartial differential equations on complex computational domains described withcomputer-aided design tools. To account for the underlying distribution of thetraining data caused by spline-based projections from the reference to thephysical domain, a variational neural solver equipped with an importancesampling scheme is developed, such that the loss function based on thediscretized energy functional obtained after the weak formulation is modifiedaccording to the sample distribution. To tackle multi-patch domains possiblyleading to solution discontinuities, the variational neural solver isadditionally combined with a domain decomposition approach based on theDiscontinuous Galerkin formulation. The proposed neural solver is verified on atoy problem and then applied to a real-world engineering test case, namely thatof electric machine simulation. The numerical results show clearly that theneural solver produces physics-conforming solutions of significantly improvedaccuracy.

A Neural Solver for Variational Problems on CAD Geometries with Application to Electric Machine Simulation