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However, its widespread applications have been inhibited by the difficulties in generating satisfactory meshes in the interior of a domain or even in generating a complete mesh. The element extraction method's primary challenge is to define element extraction rules for achieving high-quality meshes in both the boundary and the interior of a geometric domain with complex shapes. This paper presents a self-learning element extraction system, FreeMesh-S, that can automatically acquire robust and high-quality element extraction rules. Two central components enable the FreeMesh-S: (1) three primitive structures of element extraction rules, which are constructed according to boundary patterns of any geometric boundary shapes; (2) a novel self-learning schema, which is used to automatically define and refine the relationships between the parameters included in the element extraction rules, by combining an Advantage Actor-Critic (A2C) reinforcement learning network and a Feedforward Neural Network (FNN). The A2C network learns the mesh generation process through random mesh element extraction actions using element quality as a reward signal and produces high-quality elements over time. The FNN takes the mesh generated from the A2C as samples to train itself for the fast generation of high-quality elements. FreeMesh-S is demonstrated by its application to two-dimensional quad mesh generation. The meshing performance of FreeMesh-S is compared with three existing popular approaches on ten pre-defined domain boundaries. The experimental results show that even with much less domain knowledge required to develop the algorithm, FreeMesh-S outperforms those three approaches in essential indices. FreeMesh-S significantly reduces the time and expertise needed to create high-quality mesh generation algorithms.<\/jats:p>","DOI":"10.1017\/s089006042100007x","type":"journal-article","created":{"date-parts":[[2021,4,21]],"date-time":"2021-04-21T04:42:49Z","timestamp":1618980169000},"page":"180-208","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":8,"title":["A self-learning finite element extraction system based on reinforcement learning"],"prefix":"10.1017","volume":"35","author":[{"given":"Jie","family":"Pan","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2155-6107","authenticated-orcid":false,"given":"Jingwei","family":"Huang","sequence":"additional","affiliation":[]},{"given":"Yunli","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Gengdong","family":"Cheng","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6678-271X","authenticated-orcid":false,"given":"Yong","family":"Zeng","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,4,21]]},"reference":[{"key":"S089006042100007X_ref22","first-page":"177","article-title":"The application of neural network techniques to structural analysis by implementing an adaptive finite-element mesh generation","volume":"8","author":"Jadid","year":"1994","journal-title":"AI EDAM"},{"key":"S089006042100007X_ref5","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620320410"},{"key":"S089006042100007X_ref14","doi-asserted-by":"publisher","DOI":"10.2514\/6.2019-1988"},{"key":"S089006042100007X_ref35","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2020.12.019"},{"key":"S089006042100007X_ref53","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2005.01.019"},{"key":"S089006042100007X_ref36","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2006.12.002"},{"key":"S089006042100007X_ref13","doi-asserted-by":"publisher","DOI":"10.1145\/1409060.1409101"},{"key":"S089006042100007X_ref57","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8667.1993.tb00211.x"},{"key":"S089006042100007X_ref47","unstructured":"Suresh, K and Verma, CS (2019) Singularity reduction in quadrilateral meshes, Google Patents."},{"volume-title":"CUBIT Geometry and Mesh Generation Toolkit 15.2 User Documentation","year":"2016","author":"Blacker","key":"S089006042100007X_ref6"},{"key":"S089006042100007X_ref51","first-page":"2692","article-title":"Pointer networks","volume":"28","author":"Vinyals","year":"2015","journal-title":"Advances in Neural Information Processing Systems"},{"key":"S089006042100007X_ref33","first-page":"267","article-title":"A survey of unstructured mesh generation technology","volume":"239","author":"Owen","year":"1998","journal-title":"IMR"},{"key":"S089006042100007X_ref52","doi-asserted-by":"crossref","unstructured":"White, DR and Kinney, P (1997) Redesign of the paving algorithm: robustness enhancements through element by element meshing. 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