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Finite Elements Using Neural Networks and a Posteriori Error
https://orcid.org/0000-0001-6820-6898
Abstract As the finite element method requires many nodes or elements to obtain accurate results, the adaptive finite element method has been developed to obtain better results with fewer nodes, where error information is used to refine the initial mesh adaptively. In contrast to this, we propose in this paper two new methods to directly derive accurate results by artificial neural networks using information about the errors of analysis results. One of the proposed methods employs error information obtained using a posteriori error estimator to predict accurate solutions from a single analysis with a coarse mesh. The other utilizes error information obtained from comparison between two analysis results: analysis results by using a coarse mesh and those by using the corresponding refined mesh. In both methods above, the artificial neural network is employed to predict accurate results at any target point in the analysis domain based on the error information around the point. These methods are successfully tested in two-dimensional stress analyses.
Finite Elements Using Neural Networks and a Posteriori Error
https://orcid.org/0000-0001-6820-6898
Abstract As the finite element method requires many nodes or elements to obtain accurate results, the adaptive finite element method has been developed to obtain better results with fewer nodes, where error information is used to refine the initial mesh adaptively. In contrast to this, we propose in this paper two new methods to directly derive accurate results by artificial neural networks using information about the errors of analysis results. One of the proposed methods employs error information obtained using a posteriori error estimator to predict accurate solutions from a single analysis with a coarse mesh. The other utilizes error information obtained from comparison between two analysis results: analysis results by using a coarse mesh and those by using the corresponding refined mesh. In both methods above, the artificial neural network is employed to predict accurate results at any target point in the analysis domain based on the error information around the point. These methods are successfully tested in two-dimensional stress analyses.
Finite Elements Using Neural Networks and a Posteriori Error
https://orcid.org/0000-0001-6820-6898
Abstract As the finite element method requires many nodes or elements to obtain accurate results, the adaptive finite element method has been developed to obtain better results with fewer nodes, where error information is used to refine the initial mesh adaptively. In contrast to this, we propose in this paper two new methods to directly derive accurate results by artificial neural networks using information about the errors of analysis results. One of the proposed methods employs error information obtained using a posteriori error estimator to predict accurate solutions from a single analysis with a coarse mesh. The other utilizes error information obtained from comparison between two analysis results: analysis results by using a coarse mesh and those by using the corresponding refined mesh. In both methods above, the artificial neural network is employed to predict accurate results at any target point in the analysis domain based on the error information around the point. These methods are successfully tested in two-dimensional stress analyses.
Finite Elements Using Neural Networks and a Posteriori Error
Oishi, Atsuya (author) / Yagawa, Genki (author)
2020
Article (Journal)
Electronic Resource
English
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