Finite element method-enhanced neural network for forward and inverse problems
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Published:2023-05-13
Issue:1
Volume:10
Page:
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ISSN:2213-7467
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Container-title:Advanced Modeling and Simulation in Engineering Sciences
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language:en
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Short-container-title:Adv. Model. and Simul. in Eng. Sci.
Author:
Meethal Rishith E.ORCID,
Kodakkal AnoopORCID,
Khalil Mohamed,
Ghantasala Aditya,
Obst Birgit,
Bletzinger Kai-UweORCID,
Wüchner RolandORCID
Abstract
AbstractWe 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.
Funder
Technische Universität München
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computer Science Applications,Engineering (miscellaneous),Modeling and Simulation
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