Synthesis of Boundary Conditions in Polygonal Magnetic Domains Using Deep Neural Networks
In this paper, the authors approach the problem of boundary condition synthesis (also defined as field continuation) in a doubly connected domain by the use of a Neural Network-based approach. In this innovative method, given a field problem (magnetostatic, in the test case shown here), a set of Fin...
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MDPI AG
2024-12-01
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| author | Sami Barmada Paolo Di Barba Maria Evelina Mognaschi |
| author_facet | Sami Barmada Paolo Di Barba Maria Evelina Mognaschi |
| author_sort | Sami Barmada |
| collection | DOAJ |
| description | In this paper, the authors approach the problem of boundary condition synthesis (also defined as field continuation) in a doubly connected domain by the use of a Neural Network-based approach. In this innovative method, given a field problem (magnetostatic, in the test case shown here), a set of Finite Element Method simulations is performed in order to define the training set (in terms of the potential over a domain) by solving the direct problem; subsequently, the Neural Network is trained to perform the boundary condition synthesis. The performances of different Neural Networks are compared, showing the accuracy and computational efficiency of the method. Moreover, domains externally bounded by two different kinds of polygonal contours (L-shaped and three-segments, respectively) are considered. As for the latter, the effect of the concavity/convexity of the boundary is deeply investigated. To sum up, a classical field continuation problem turns out to be revisited and solved with an innovative approach, based on deep learning. |
| format | Article |
| id | doaj-art-041f3a83c1634a2a8504acf508e6bbd2 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-041f3a83c1634a2a8504acf508e6bbd22024-12-13T16:27:57ZengMDPI AGMathematics2227-73902024-12-011223385110.3390/math12233851Synthesis of Boundary Conditions in Polygonal Magnetic Domains Using Deep Neural NetworksSami Barmada0Paolo Di Barba1Maria Evelina Mognaschi2Department of Energy, Systems, Territory and Construction Engineering, University of Pisa, 56126 Pisa, Italy 2 Department of Electrical, Computer and Biomedical Engineering, University of Pavia, 27100 Pavia, ItalyDepartment of Electrical, Computer and Biomedical Engineering, University of Pavia, 27100 Pavia, ItalyDepartment of Electrical, Computer and Biomedical Engineering, University of Pavia, 27100 Pavia, ItalyIn this paper, the authors approach the problem of boundary condition synthesis (also defined as field continuation) in a doubly connected domain by the use of a Neural Network-based approach. In this innovative method, given a field problem (magnetostatic, in the test case shown here), a set of Finite Element Method simulations is performed in order to define the training set (in terms of the potential over a domain) by solving the direct problem; subsequently, the Neural Network is trained to perform the boundary condition synthesis. The performances of different Neural Networks are compared, showing the accuracy and computational efficiency of the method. Moreover, domains externally bounded by two different kinds of polygonal contours (L-shaped and three-segments, respectively) are considered. As for the latter, the effect of the concavity/convexity of the boundary is deeply investigated. To sum up, a classical field continuation problem turns out to be revisited and solved with an innovative approach, based on deep learning.https://www.mdpi.com/2227-7390/12/23/3851field continuation problemdeep learningmagnetic field |
| spellingShingle | Sami Barmada Paolo Di Barba Maria Evelina Mognaschi Synthesis of Boundary Conditions in Polygonal Magnetic Domains Using Deep Neural Networks Mathematics field continuation problem deep learning magnetic field |
| title | Synthesis of Boundary Conditions in Polygonal Magnetic Domains Using Deep Neural Networks |
| title_full | Synthesis of Boundary Conditions in Polygonal Magnetic Domains Using Deep Neural Networks |
| title_fullStr | Synthesis of Boundary Conditions in Polygonal Magnetic Domains Using Deep Neural Networks |
| title_full_unstemmed | Synthesis of Boundary Conditions in Polygonal Magnetic Domains Using Deep Neural Networks |
| title_short | Synthesis of Boundary Conditions in Polygonal Magnetic Domains Using Deep Neural Networks |
| title_sort | synthesis of boundary conditions in polygonal magnetic domains using deep neural networks |
| topic | field continuation problem deep learning magnetic field |
| url | https://www.mdpi.com/2227-7390/12/23/3851 |
| work_keys_str_mv | AT samibarmada synthesisofboundaryconditionsinpolygonalmagneticdomainsusingdeepneuralnetworks AT paolodibarba synthesisofboundaryconditionsinpolygonalmagneticdomainsusingdeepneuralnetworks AT mariaevelinamognaschi synthesisofboundaryconditionsinpolygonalmagneticdomainsusingdeepneuralnetworks |