Finite element method-enhanced neural network for forward and inverse problems

Advanced Modeling and Simulation in Engineering Sciences

Research Article

Anoop Kodakkal¹  Aditya Ghantasala¹  Kai-Uwe Bletzinger¹  Roland Wüchner²  Mohamed Khalil³  Birgit Obst³  Rishith E. Meethal⁴ 

[1] Chair of Structural Analysis, Technical University of Munich, Munich, Germany;Institute of Structural Analysis, Technische Universität Braunschweig, Braunschweig, Germany;Technology, Siemens AG, Munich, Germany;Technology, Siemens AG, Munich, Germany;Chair of Structural Analysis, Technical University of Munich, Munich, Germany;

关键词: Hybrid models;    Informed machine learning;    FEM-based neural network;    Self-supervised learning;   

DOI  :  10.1186/s40323-023-00243-1

 received in 2022-06-23, accepted in 2023-03-08,  发布年份 2023

来源: Springer

【 摘 要 】

We introduce a novel hybrid methodology that combines 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 models in real-time simulation, uncertainty quantification, and optimization in the case of forward problems. It can be used to update models for inverse problems. The method is demonstrated with examples and the accuracy of the results and performance is compared to the conventional way of network training and the classical finite element method. An application of the forward-solving algorithm is demonstrated for the uncertainty quantification of wind effects on a high-rise buildings. The inverse algorithm is demonstrated in the speed-dependent bearing coefficient identification of fluid bearings. Hybrid methodology of this kind will serve as a paradigm shift in the simulation methods currently used.

【 授权许可】

CC BY   
© The Author(s) 2023

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