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A self-learning finite element extraction system based on reinforcement learning

Published online by Cambridge University Press:  21 April 2021

Jie Pan ,
Jingwei Huang Open the ORCID record for Jingwei Huang [Opens in a new window] ,
Yunli Wang ,
Gengdong Cheng  and
Yong Zeng Open the ORCID record for Yong Zeng [Opens in a new window]
Jie Pan
Affiliation:
Concordia Institute for Information Systems Engineering, Concordia University, Montreal, QC, Canada
Jingwei Huang
Affiliation:
Department of Engineering Management & Systems Engineering, Old Dominion University, Norfolk, VA, USA
Yunli Wang
Affiliation:
Digital Technologies Research Centre, National Research Council Canada, Ottawa, ON, Canada
Gengdong Cheng
Affiliation:
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, People's Republic of China
Yong Zeng*
Affiliation:
Concordia Institute for Information Systems Engineering, Concordia University, Montreal, QC, Canada
*
Author for correspondence: Yong Zeng, E-mail: yong.zeng@concordia.ca
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Abstract

Automatic generation of high-quality meshes is a base of CAD/CAE systems. The element extraction is a major mesh generation method for its capabilities to generate high-quality meshes around the domain boundary and to control local mesh densities. 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.

Keywords

Element extractionreinforcement learningself-learning systemsmart designsmart mesh generation
Type
Research Article
Information
AI EDAM , Volume 35 , Special Issue 2: Thematic Collection: Smart Design of Smart Systems , May 2021 , pp. 180 - 208
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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References

Akhras, G (2000) Smart materials and smart systems for the future. Canadian Military Journal 1, 25–31.Google Scholar
Atalay, FB, Ramaswami, S and Xu, D (2008) Quadrilateral meshes with bounded minimum angle. In Proceedings of the 17th International Meshing Roundtable. Springer, pp. 73–91.CrossRefGoogle Scholar
Baehmann, PL, Wittchen, SL, Shephard, MS, Grice, KR and Yerry, MA (1987) Robust, geometrically based, automatic two-dimensional mesh generation. International Journal for Numerical Methods in Engineering 24, 1043–1078.CrossRefGoogle Scholar
Bern, M and Eppstein, D (2000) Quadrilateral meshing by circle packing. International Journal of Computational Geometry & Applications 10, 347–360.CrossRefGoogle Scholar
Blacker, TD and Stephenson, MB (1991) Paving: a new approach to automated quadrilateral mesh generation. International Journal for Numerical Methods in Engineering 32, 811–847.CrossRefGoogle Scholar
Blacker, TD, Owen, SJ, Staten, ML and Morris, R (2016) CUBIT Geometry and Mesh Generation Toolkit 15.2 User Documentation. United States: Sandia National Lab.Google Scholar
Bommes, D, Lévy, B, Pietroni, N and Zorin, D (2013) Quad-mesh generation and processing: a survey. Computer Graphics Forum 32, 51–76.CrossRefGoogle Scholar
Brewer, ML, Diachin, LF, Knupp, PM, Leurent, T and Melander, DJ (2003) The Mesquite Mesh Quality Improvement Toolkit. In IMR, Sandia National Lab, pp. 239–259.Google Scholar
Capuano, G and Rimoli, JJ (2019) Smart finite elements: a novel machine learning application. Computer Methods in Applied Mechanics and Engineering 345, 363–381.CrossRefGoogle Scholar
Catmull, E and Clark, J (1978) Recursively generated B-spline surfaces on arbitrary topological meshes. Computer-Aided Design 10, 350–355.CrossRefGoogle Scholar
Chedid, R and Najjar, N (1996) Automatic finite-element mesh generation using artificial neural networks-part I: prediction of mesh density. IEEE Transactions on Magnetics 32, 5173–5178.CrossRefGoogle Scholar
Chew, LP (1989) Constrained Delaunay triangulations. Algorithmica 4, 97–108.CrossRefGoogle Scholar
Daniels, J, Silva, CT, Shepherd, J and Cohen, E (2008) Quadrilateral mesh simplification. ACM Transactions on Graphics (TOG) 27, 1–9.CrossRefGoogle Scholar
Docampo-Sánchez, J and Haimes, R (2019) Towards fully regular quad mesh generation. AIAA Scitech 2019 Forum.CrossRefGoogle Scholar
Dolšak, B (2002) Finite element mesh design expert system. Knowledge-Based Systems 15, 315–322.CrossRefGoogle Scholar
Ebeida, MS, Karamete, K, Mestreau, E and Dey, S (2010) Q-TRAN: a new approach to transform triangular meshes into quadrilateral meshes locally. In Proceedings of the 19th International Meshing Roundtable, Springer, pp. 23–34.CrossRefGoogle Scholar
Garimella, RV, Shashkov, MJ and Knupp, PM (2004) Triangular and quadrilateral surface mesh quality optimization using local parametrization. Computer Methods in Applied Mechanics and Engineering 193, 913–928.CrossRefGoogle Scholar
Geuzaine, C and Remacle, JF (2009) Gmsh: a 3-D finite element mesh generator with built-in pre- and post-processing facilities. International Journal for Numerical Methods in Engineering 79, 1309–1331.CrossRefGoogle Scholar
Gordon, WJ and Hall, CA (1973) Construction of curvilinear co-ordinate systems and applications to mesh generation. International Journal for Numerical Methods in Engineering 7, 461–477.CrossRefGoogle Scholar
Grondman, I, Busoniu, L, Lopes, GA and Babuska, R (2012) A survey of actor-critic reinforcement learning: standard and natural policy gradients. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews) 42, 1291–1307.CrossRefGoogle Scholar
Hanocka, R, Hertz, A, Fish, N, Giryes, R, Fleishman, S and Cohen-Or, D (2019) MeshCNN: a network with an edge. ACM Transactions on Graphics (TOG) 38, 1–12.Google Scholar
Jadid, MN and Fairbairn, DR (1994) The application of neural network techniques to structural analysis by implementing an adaptive finite-element mesh generation. AI EDAM 8, 177–191.Google Scholar
Johnen, A (2016) Indirect quadrangular mesh generation and validation of curved finite elements (PhD Thesis). Liège, Belgique: Université de Liège.Google Scholar
Kaelbling, LP, Littman, ML and Moore, AW (1996) Reinforcement learning: a survey. Journal of Artificial Intelligence Research 4, 237–285.CrossRefGoogle Scholar
Kahneman, D (2011) Thinking, Fast and Slow. New York, NY: Farrar, Straus and Giroux.Google Scholar
Knupp, PM (2000) Achieving finite element mesh quality via optimization of the Jacobian matrix norm and associated quantities. Part II – a framework for volume mesh optimization and the condition number of the Jacobian matrix. International Journal for Numerical Methods in Engineering 48, 1165–1185.3.0.CO;2-Y>CrossRefGoogle Scholar
Lévy, B and Liu, Y (2010) Lp centroidal voronoi tessellation and its applications. ACM Transactions on Graphics (TOG) 29, 1–11.CrossRefGoogle Scholar
Liang, X and Zhang, Y (2012) Matching interior and exterior all-quadrilateral meshes with guaranteed angle bounds. Engineering with Computers 28, 375–389.CrossRefGoogle Scholar
Liang, X, Ebeida, MS and Zhang, Y (2009) Guaranteed-quality all-quadrilateral mesh generation with feature preservation. In Proceedings of the 18th International Meshing Roundtable, Springer, pp. 45–63.CrossRefGoogle Scholar
Littman, ML (2015) Reinforcement learning improves behaviour from evaluative feedback. Nature 521, 445–451.CrossRefGoogle ScholarPubMed
Manevitz, L, Yousef, M and Givoli, D (1997) Finite–element mesh generation using self–organizing neural networks. Computer-Aided Civil and Infrastructure Engineering 12, 233–250.CrossRefGoogle Scholar
Nechaeva, O (2006) Composite algorithm for adaptive mesh construction based on self-organizing maps. In International Conference on Artificial Neural Networks, Springer, pp. 445–454.CrossRefGoogle Scholar
Owen, SJ (1998) A survey of unstructured mesh generation technology. IMR 239, 267.Google Scholar
Owen, SJ, Staten, ML, Canann, SA and Saigal, S (1999) Q-Morph: an indirect approach to advancing front quad meshing. International Journal for Numerical Methods in Engineering 44, 1317–1340.3.0.CO;2-N>CrossRefGoogle Scholar
Papagiannopoulos, A, Clausen, P and Avellan, F (2021) How to teach neural networks to mesh: application on 2-D simplicial contours. Neural Networks 136, 152–179.CrossRefGoogle ScholarPubMed
Park, C, Noh, J-S, Jang, I-S and Kang, JM (2007) A new automated scheme of quadrilateral mesh generation for randomly distributed line constraints. Computer-Aided Design 39, 258–267.CrossRefGoogle Scholar
Pébay, PP, Thompson, D, Shepherd, J and Grosland, NM (2008) New applications of the verdict library for standardized mesh verification pre, post, and end-to-end processing. In Proceedings of the 16th International Meshing Roundtable, IMR 2007, pp. 535–552.CrossRefGoogle Scholar
Peters, J and Reif, U (1997) The simplest subdivision scheme for smoothing polyhedra. ACM Transactions on Graphics (TOG) 16, 420–431.CrossRefGoogle Scholar
Prautzsch, H and Chen, Q (2011) Analyzing midpoint subdivision. Computer Aided Geometric Design 28, 407–419.CrossRefGoogle Scholar
Remacle, J-F, Lambrechts, J, Seny, B, Marchandise, E, Johnen, A and Geuzainet, C (2012) Blossom-Quad: a non-uniform quadrilateral mesh generator using a minimum-cost perfect-matching algorithm. International Journal for Numerical Methods in Engineering 89, 1102–1119.CrossRefGoogle Scholar
Remacle, J-F, Henrotte, F, Carrier-Baudouin, T and Mouton, T (2013) A frontal delaunay quad mesh generator using the L∞ norm. International Journal for Numerical Methods in Engineering 94, 494–512.CrossRefGoogle Scholar
Roca, X and Loseille, A (2019) 27th International Meshing Roundtable, Vol. 127. Albuquerque, NM, USA: Springer.CrossRefGoogle Scholar
Rushdi, AA, Mitchell, SA, Mahmoud, AH, Bajaj, CC and Ebeida, MS (2017) All-quad meshing without cleanup. Computer-Aided Design 85, 83–98.CrossRefGoogle Scholar
Sarrate Ramos, J, Ruiz-Gironés, E and Roca Navarro, FJ (2014) Unstructured and semi-structured hexahedral mesh generation methods. Computational Technology Reviews 10, 35–64.CrossRefGoogle Scholar
Shewchuk, JR (2012) Unstructured mesh generation. Combinatorial Scientific Computing 12, 2.Google Scholar
Shimada, K, Liao, J-H and Itoh, T (1998) Quadrilateral Meshing with Directionality Control through the Packing of Square Cells. In IMR, Citeseer, pp. 61–75.Google Scholar
Suresh, K and Verma, CS (2019) Singularity reduction in quadrilateral meshes, Google Patents.Google Scholar
Sutton, RS and Barto, AG (2018) Reinforcement Learning: An Introduction. Cambridge, Massachusetts, USA: MIT Press.Google Scholar
Thompson, JF, Soni, BK and Weatherill, NP (1998) Handbook of Grid Generation. Boca Raton, Florida, USA: CRC Press.CrossRefGoogle Scholar
Verma, CS and Suresh, K (2017) A robust combinatorial approach to reduce singularities in quadrilateral meshes. Computer Aided Design 85, 99–110.CrossRefGoogle Scholar
Vinyals, O, Fortunato, M and Jaitly, N (2015) Pointer networks. Advances in Neural Information Processing Systems 28, 2692–2700.Google Scholar
White, DR and Kinney, P (1997) Redesign of the paving algorithm: robustness enhancements through element by element meshing. In 6th International Meshing Roundtable, pp. 323–335.Google Scholar
Yao, S, Yan, B, Chen, B and Zeng, Y (2005) An ANN-based element extraction method for automatic mesh generation. Expert Systems with Applications 29, 193–206.CrossRefGoogle Scholar
Zeng, Y (2004) Environment-based formulation of design problem. Journal of Integrated Design and Process Science 8, 45–63.Google Scholar
Zeng, Y (2015) Environment-Based Design (EBD): a Methodology for Transdisciplinary Design.Journal of Integrated Design and Process Science 19, 5–24.CrossRefGoogle Scholar
Zeng, Y and Cheng, G (1991) On the logic of design. Design Studies 12, 137–141.CrossRefGoogle Scholar
Zeng, Y and Cheng, G (1993) Knowledge-based free mesh generation of quadrilateral elements in two-dimensional domains. Computer-Aided Civil and Infrastructure Engineering 8, 259–270.CrossRefGoogle Scholar
Zeng, Y and Yao, S (2009) Understanding design activities through computer simulation. Advanced Engineering Informatics 23, 294–308.CrossRefGoogle Scholar
Zhang, K, Cheng, G and Xu, L (2019) Topology optimization considering overhang constraint in additive manufacturing. Computers & Structures 212, 86–100.CrossRefGoogle Scholar
Zhang, Z, Wang, Y, Jimack, PK and Wang, H (2020) MeshingNet: a new mesh generation method based on deep learning. In International Conference on Computational Science, Springer, pp. 186–198.Google Scholar
Zhang, L, Cheng, L, Li, H and Liu, WK (2021) Hierarchical deep-learning neural networks: finite elements and beyond. Computational Mechanics 67, 207–230.CrossRefGoogle Scholar
Zhu, JZ, Zienkiewicz, OC, Hinton, E and Wu, J (1991) A new approach to the development of automatic quadrilateral mesh generation. International Journal for Numerical Methods in Engineering 32, 849–866.CrossRefGoogle Scholar