Finite element method-enhanced neural network for forward and inverse problems
Abstract 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 ne...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-05-01
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| Series: | Advanced Modeling and Simulation in Engineering Sciences |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s40323-023-00243-1 |
| _version_ | 1797827426504409088 |
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| author | Rishith E. Meethal Anoop Kodakkal Mohamed Khalil Aditya Ghantasala Birgit Obst Kai-Uwe Bletzinger Roland Wüchner |
| author_facet | Rishith E. Meethal Anoop Kodakkal Mohamed Khalil Aditya Ghantasala Birgit Obst Kai-Uwe Bletzinger Roland Wüchner |
| author_sort | Rishith E. Meethal |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-04-09T12:48:06Z |
| format | Article |
| id | doaj.art-22dd9c53df344dc98c91e8653652d31c |
| institution | Directory Open Access Journal |
| issn | 2213-7467 |
| language | English |
| last_indexed | 2024-04-09T12:48:06Z |
| publishDate | 2023-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advanced Modeling and Simulation in Engineering Sciences |
| spelling | doaj.art-22dd9c53df344dc98c91e8653652d31c2023-05-14T11:22:44ZengSpringerOpenAdvanced Modeling and Simulation in Engineering Sciences2213-74672023-05-0110112310.1186/s40323-023-00243-1Finite element method-enhanced neural network for forward and inverse problemsRishith E. Meethal0Anoop Kodakkal1Mohamed Khalil2Aditya Ghantasala3Birgit Obst4Kai-Uwe Bletzinger5Roland Wüchner6Technology, Siemens AGChair of Structural Analysis, Technical University of MunichTechnology, Siemens AGChair of Structural Analysis, Technical University of MunichTechnology, Siemens AGChair of Structural Analysis, Technical University of MunichInstitute of Structural Analysis, Technische Universität BraunschweigAbstract 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.https://doi.org/10.1186/s40323-023-00243-1Hybrid modelsInformed machine learningFEM-based neural networkSelf-supervised learning |
| spellingShingle | Rishith E. Meethal Anoop Kodakkal Mohamed Khalil Aditya Ghantasala Birgit Obst Kai-Uwe Bletzinger Roland Wüchner Finite element method-enhanced neural network for forward and inverse problems Advanced Modeling and Simulation in Engineering Sciences Hybrid models Informed machine learning FEM-based neural network Self-supervised learning |
| title | Finite element method-enhanced neural network for forward and inverse problems |
| title_full | Finite element method-enhanced neural network for forward and inverse problems |
| title_fullStr | Finite element method-enhanced neural network for forward and inverse problems |
| title_full_unstemmed | Finite element method-enhanced neural network for forward and inverse problems |
| title_short | Finite element method-enhanced neural network for forward and inverse problems |
| title_sort | finite element method enhanced neural network for forward and inverse problems |
| topic | Hybrid models Informed machine learning FEM-based neural network Self-supervised learning |
| url | https://doi.org/10.1186/s40323-023-00243-1 |
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