Abstract This work develops a computational framework that combines physics-informed neural networks with multi-patch isogeometric mappings to solve partial differential equations on complex computer-aided design geometries. The method utilizes patch-local neural networks that operate on the parametric space of each patch, i.e. the reference domain of the local isogeometric map. A custom output layer enables the strong imposition of Dirichlet boundary conditions. Solution conformity across interfaces between non-uniform rational B-spline patches is enforced using dedicated interface neural networks. Training is performed using the variational framework by minimizing the energy functional derived after the weak form of the partial differential equation. The effectiveness of the suggested method is demonstrated on a benchmark problem and on two highly non-trivial engineering applications. The results show excellent agreement to reference solutions obtained with high-fidelity finite element solvers, thus highlighting the potential of the suggested neural solver to tackle complex engineering problems given the corresponding computer-aided design models.
Tresckow et al. (Tue,) studied this question.