# Finite Element Method-enhanced Neural Network for Forward and Inverse Problems

@article{Meethal2022FiniteEM, title={Finite Element Method-enhanced Neural Network for Forward and Inverse Problems}, author={Rishith Ellath Meethal and Birgit Obst and Mohamed Khalil and Aditya Ghantasala and Anoop Kodakkal and Kai-Uwe Bletzinger and Roland W{\"u}chner}, journal={ArXiv}, year={2022}, volume={abs/2205.08321} }

We introduce a novel hybrid methodology combining classical ﬁnite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from ﬁnite element methods and custom loss functions from neural networks are merged to form the algorithm. The Finite Element Method-enhanced Neural Network hybrid model (FEM-NN hybrid) is data-efﬁcient and physics conforming. The proposed methodology can be used for surrogate…

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