Phương pháp gradient chính xác sâu và mạng chú ý đồ thị cho tối ưu hóa hình học của các cấu trúc lưới

Springer Science and Business Media LLC - Tập 53 Số 17 - Trang 19809-19826 - 2023
Kupwiwat, Chi-tathon1, Hayashi, Kazuki1, Ohsaki, Makoto1
1Department of Architecture and Architectural Engineering, Graduate School of Engineering, Kyoto University, Kyoto, Japan

Tóm tắt

Bài báo này đề xuất một phương pháp kết hợp giữa gradient chính xác sâu (DDPG) và mạng chú ý đồ thị (GAT) để tối ưu hóa hình học của các vỏ lưới có hình dạng bề mặt được định nghĩa bởi mạng điều khiển Bézier. Vấn đề tối ưu hóa được xây dựng để giảm thiểu năng lượng biến dạng của các cấu trúc lưới, với chiều cao của các điểm điều khiển Bézier được sử dụng làm biến thiết kế. Thông tin về các vỏ lưới, bao gồm cấu hình điểm nút, thuộc tính phần tử và lực nội tại, cùng với mạng điều khiển Bézier, bao gồm các điểm điều khiển và mạng điều khiển, được đại diện dưới dạng đồ thị bằng cách sử dụng ma trận đặc trưng nút, ma trận kề, và ma trận kề có trọng số. Một tác nhân DDPG được thiết kế đặc biệt sử dụng GAT và các phép xử lý ma trận để quan sát trạng thái của cấu trúc thông qua các đồ thị, và quyết định điểm điều khiển Bézier nào và cách di chuyển chúng. Tác nhân được huấn luyện để xuất sắc trong nhiệm vụ này thông qua tín hiệu thưởng được tính toán từ các thay đổi trong năng lượng biến dạng trong mỗi bước tối ưu hóa. Như được thể hiện trong các ví dụ số, tác nhân đã được huấn luyện có thể tối ưu hóa hiệu quả các cấu trúc có kích thước, mạng điều khiển, cấu hình và hình học ban đầu khác nhau so với những gì được sử dụng trong quá trình huấn luyện. Hiệu suất của tác nhân đã được huấn luyện là cạnh tranh so với tối ưu hóa bầy đàn và làm nguội mô phỏng mặc dù sử dụng chi phí tính toán thấp hơn.

Từ khóa

#tối ưu hóa hình học #cấu trúc lưới #sâu gradient chính xác #mạng chú ý đồ thị #điều khiển Bézier

Tài liệu tham khảo

citation_title=An introduction to structural optimization; citation_publication_date=2010; citation_id=CR1; citation_author=PW Christensen; citation_author=A Klarbring; citation_publisher=Springer Ohsaki M, Swan CC (2002) Topology and geometry optimization of trusses and frames. In: Scott AB (ed) Recent advances in optimal structural design. American Society of Civil Engineers, Virginia, pp 97–123 Ohsaki M (2010) Optimization of finite dimensional structures. CRC Press, Boca Raton, pp 259–313. https://doi.org/10.1201/EBK1439820032 citation_journal_title=J Struct Eng; citation_title=Shape optimization of skeletal structures: a review; citation_author=BH Topping; citation_volume=109; citation_issue=8; citation_publication_date=1983; citation_pages=1933-1951; citation_doi=10.1061/(ASCE)0733-9445(1983)109:8(1933); citation_id=CR4 citation_journal_title=Comput Methods Appl Mech Eng; citation_title=Truss shape optimization with multiple displacement constraints; citation_author=D Wang, WH Zhang, JS Jiang; citation_volume=191; citation_publication_date=2002; citation_pages=3597-3361; citation_doi=10.1016/S0045-7825(02)00297-9; citation_id=CR5 citation_journal_title=Eng Appl Artif Intell; citation_title=Shape optimization of free-form steel space-frame roof structures with complex geometries using evolutionary computing; citation_author=M Kociecki, H Adeli; citation_volume=38; citation_publication_date=2015; citation_pages=168-182; citation_doi=10.1016/j.engappai.2014.10.012; citation_id=CR6 citation_title=Structural sensitivity analysis and optimization 1: linear systems; citation_publication_date=2005; citation_id=CR7; citation_author=KK Choi; citation_author=NH Kim; citation_publisher=Springer citation_journal_title=Am Inst Aeronaut Astronaut J; citation_title=Sensitivity analysis of discrete structural systems; citation_author=H Adelman, R Haftka; citation_volume=24; citation_publication_date=1986; citation_pages=823-832; citation_doi=10.2514/3.48671; citation_id=CR8 citation_journal_title=Comput Methods Appl Mech Eng; citation_title=Efficient sensitivity analysis for structural optimization; citation_author=U Kirsch; citation_volume=117; citation_publication_date=1994; citation_pages=143-156; citation_doi=10.1016/0045-7825(94)90080-9; citation_id=CR9 citation_journal_title=Int J Numer Methods Eng; citation_title=Sensitivity analysis of frame structures (virtual distortion method approach); citation_author=J Putresza, P Kolakowski; citation_volume=43; citation_publication_date=1998; citation_pages=1085-1108; citation_doi=10.1002/1097-0207(20010228)50:6%3C1307::AID-NME38%3E3.0.CO;2-Q; citation_id=CR10 citation_journal_title=J Struct Eng; citation_title=Plane frame optimum design environment based on genetic algorithm; citation_author=WM Jenkins; citation_volume=118; citation_publication_date=1992; citation_pages=3103-3112; citation_doi=10.1061/(ASCE)0733-9445(1992)118:11(3103); citation_id=CR11 citation_journal_title=Struct Multidiscip Optim; citation_title=Evolving structural design solutions using an implicit redundant genetic algorithm; citation_author=A Raich, J Ghaboussi; citation_volume=20; citation_publication_date=2000; citation_pages=222-231; citation_doi=10.1007/s001580050150; citation_id=CR12 citation_journal_title=Int J Numer Methods Eng; citation_title=Analysis, design and optimization of structures using force method and genetic algorithm; citation_author=A Kaveh, H Rahami; citation_volume=65; citation_issue=10; citation_publication_date=2006; citation_pages=1570-1584; citation_doi=10.1002/nme.1506; citation_id=CR13 citation_journal_title=J Int Assoc Shell Spat Struct; citation_title=Computational morphogenesis of free form shells; citation_author=T Kimura, H Ohmori; citation_volume=49; citation_issue=3; citation_publication_date=2008; citation_pages=175-180; citation_id=CR14 citation_journal_title=Comput Methods Appl Mech Eng; citation_title=A NURBS-based inverse analysis for reconstruction of nonlinear deformations of thin shell structures; citation_author=N Vu-Bac, TX Duong, T Lahmer, X Zhuang, RA Sauer, HS Parke, T Rabczuk; citation_volume=331; citation_publication_date=2018; citation_pages=427-455; citation_doi=10.1016/j.cma.2017.09.034; citation_id=CR15 citation_journal_title=Comm Soc Math Kharkow; citation_title=Démonstration du théorème de weierstrass fondée sur le calcul des probabilités; citation_author=S Bernstein; citation_volume=13; citation_publication_date=1912; citation_pages=1-2; citation_id=CR16 citation_journal_title=Revue Européenne des Éléments Finis; citation_title=Shape optimization of shell structures; citation_author=E Ramm, KU Bletzinger, R Reitinger; citation_volume=2; citation_issue=3; citation_publication_date=1993; citation_pages=377-398; citation_doi=10.1080/12506559.1993.10511083; citation_id=CR17 citation_title=Measures of fairness for curves and surfaces; citation_inbook_title=Designing fair curves and surfaces; citation_publication_date=1994; citation_pages=75-122; citation_id=CR18; citation_author=JA Roulier; citation_author=T Rondo; citation_publisher=SIAM citation_journal_title=Int J Space Struct; citation_title=Shape optimization of a double-layer space truss described by a parametric surface; citation_author=M Ohsaki, T Nakamura, M Kohiyama; citation_volume=12; citation_publication_date=1997; citation_pages=109-119; citation_doi=10.1177/026635119701200205; citation_id=CR19 citation_journal_title=J Int Assoc Shell Spat Struct; citation_title=Fairness metrics for shape optimization of ribbed shells; citation_author=M Ohsaki, M Hayashi; citation_volume=41; citation_issue=1; citation_publication_date=2000; citation_pages=31-39; citation_id=CR20 citation_journal_title=Psycol Rev; citation_title=The perceptron: a probabilistic model for information storage and organization in the brain; citation_author=F Rosenblatt; citation_volume=65; citation_issue=6; citation_publication_date=1958; citation_pages=386-408; citation_doi=10.1037/h0042519; citation_id=CR21 citation_journal_title=Sov Autom Control; citation_title=The group method of data handling – a rival of the of stochastic approximation; citation_author=AG Ivakhnenko; citation_volume=13; citation_issue=3; citation_publication_date=1968; citation_pages=43-55; citation_id=CR22 citation_title=Deep learning; citation_publication_date=2016; citation_id=CR23; citation_author=I Goodfellow; citation_author=Y Bengio; citation_author=A Courville; citation_publisher=MIT Press citation_journal_title=Comput-Aided Civil Infrastruct Eng; citation_title=Neural networks in structural engineering; citation_author=RD Vanluchene, R Sun; citation_volume=5; citation_issue=3; citation_publication_date=1990; citation_pages=207-215; citation_doi=10.1111/j.1467-8667.1990.tb00377.x; citation_id=CR24 citation_title=Application of neural nets in structural optimization; citation_inbook_title=Optimization of large structural systems. NATO ASI series vol 231; citation_publication_date=1993; citation_pages=731-745; citation_id=CR25; citation_author=L Berke; citation_author=P Hajela citation_journal_title=Finite Elem Anal Des; citation_title=A machine learning-based surrogate model for optimization of truss structures with geometrically nonlinear behavior; citation_author=TH Mai, J Kang, J Lee; citation_volume=196; citation_publication_date=2021; citation_pages=103572; citation_doi=10.1016/j.finel.2021.103572; citation_id=CR26 citation_journal_title=Front Built Environ; citation_title=Machine learning in structural design: an opinionated review; citation_author=MC Christian; citation_volume=8; citation_publication_date=2022; citation_pages=815717; citation_doi=10.3389/fbuil.2022.815717; citation_id=CR27 citation_journal_title=Structures; citation_title=Comparison between human-defined and ai-generated design spaces for the optimisation of shell structures; citation_author=G Mirra, A Pugnale; citation_volume=34; citation_publication_date=2021; citation_pages=2950-2961; citation_doi=10.1016/j.istruc.2021.09.058; citation_id=CR28 citation_journal_title=Found Trends Mach Learn; citation_title=An introduction to variational autoencoders; citation_author=PD Kingma, M Welling; citation_volume=12; citation_issue=4; citation_publication_date=2019; citation_pages=307-392; citation_doi=10.1561/2200000056; citation_id=CR29 citation_journal_title=Comput Methods Appl Mech Eng; citation_title=An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications; citation_author=EP Samaniego, C Anitescu, S Goswami, VM Nguyen-Thanh, H Guo, KM Hamdia, T Rabczuk, X Zhuang; citation_volume=362; citation_publication_date=2020; citation_pages=112790; citation_doi=10.1016/j.cma.2019.112790; citation_id=CR30 citation_journal_title=Autom Constr; citation_title=Machine learning assisted evaluations in structural design and construction; citation_author=H Zheng, V Moosavi, M Akbarzadeh; citation_volume=119; citation_publication_date=2020; citation_pages=103346; citation_doi=10.1016/j.autcon.2020.103346; citation_id=CR31 Fuhrimann L, Moosavi V, Ohlbrock P O, D’acunto P (2018) Data-driven design: exploring new structural forms using machine learning and graphic statics. In: Proceedings of international association for shell and spatial structures, pp. 1–8 citation_journal_title=Comput Mech; citation_title=A generalized Bayesian regularization network approach on characterization of geometric defects in lattice structures for topology optimization in preliminary design of 3D printing; citation_author=Y Xie, S Li, CT Wu, D Lyu, C Wang, D Zeng; citation_volume=69; citation_publication_date=2022; citation_pages=1191-1212; citation_doi=10.1007/s00466-021-02137-8; citation_id=CR33 Lillicrap T P, Hunt J J, Pritzel A, Heess N, Erez T, Tassa Y, Silver D, Wierstra D (2016) Continuous control with deep reinforcement learning. In: International conference on learning representations (poster) citation_journal_title=J Struct Eng B Archit Inst Jpn; citation_title=Fundamental study on morphogenesis of shell structure using reinforcement; citation_author=C Kupwiwat, K Yamamoto; citation_volume=67B; citation_publication_date=2021; citation_pages=211-218; citation_id=CR35 citation_journal_title=Front Built Environ; citation_title=Reinforcement learning and graph embedding for binary truss topology optimization under stress and displacement constraints; citation_author=K Hayashi, M Ohsaki; citation_volume=6; citation_publication_date=2021; citation_pages=59; citation_doi=10.3389/fbuil.2020.00059; citation_id=CR36 citation_journal_title=Adv Eng Softw; citation_title=Machine-specified ground structures for topology optimization of binary trusses using graph embedding policy network; citation_author=S Zhu, M Ohsaki, K Hayashi, X Guo; citation_volume=159; citation_publication_date=2021; citation_pages=103032; citation_doi=10.1016/j.advengsoft.2021.103032; citation_id=CR37 citation_journal_title=Front Built Environ; citation_title=Deep deterministic policy gradient and graph convolutional network for bracing direction optimization of grid shells; citation_author=C Kupwiwat, K Hayashi, M Ohsaki; citation_volume=8; citation_publication_date=2022; citation_pages=899072; citation_doi=10.3389/fbuil.2022.899072; citation_id=CR38 Gilmer J, Schoenholz S, Riley P, Vinyals O, Dahl G (2017) Neural message passing for quantum chemistry. In: Proceedings of international conference on machine learning, vol 70, pp. 1263–1272 Kipf T N, Welling M (2017) Semi-supervised classification with graph convolutional networks. In: Proceedings of international conference on learning representations, pp. 1–14 Veličković P, Cucurull G, Casanova A, Romero A, Lio P, Bengio Y (2017) Graph attention networks. In: Proceedings of international conference on learning representations, pp. 1–12 Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez A N, Kaiser L, Polosukhin I (2017) Attention is all you need. In: Proceedings of advances in neural information processing systems, pp. 5998–6008 citation_journal_title=Proc IEEE Int Conf Data Mining; citation_title=Community attention network for semi-supervised node classification; citation_author=Z Yu, H Wang, Y Liu, C Böhm, J Shao; citation_volume=17; citation_issue=20; citation_publication_date=2020; citation_pages=1382-1387; citation_doi=10.1109/ICDM50108.2020.00181; citation_id=CR43 citation_journal_title=Proc Int Conf Artif Neural Netw; citation_title=Signed graph attention networks; citation_author=J Huang, H Shen, L Hou, X Cheng; citation_volume=28; citation_publication_date=2019; citation_pages=566-577; citation_doi=10.1007/978-3-030-30493-5_53; citation_id=CR44 citation_journal_title=IEEE Trans Knowl Data Eng; citation_title=Higher-order interaction goes neural: a substructure assembling graph attention network for graph classification; citation_author=J Gao, J Gao, X Ying, M Lu, J Wang; citation_volume=35; citation_issue=2; citation_publication_date=2021; citation_pages=1594-1608; citation_doi=10.1109/TKDE.2021.3105544; citation_id=CR45 citation_title=Reinforcement learning, an introduction; citation_publication_date=2018; citation_id=CR46; citation_author=RS Sutton; citation_author=GB Andrew; citation_publisher=MIT Press citation_journal_title=Indiana Univ Math J; citation_title=A markovian decision process; citation_author=R Bellman; citation_volume=6; citation_issue=4; citation_publication_date=1957; citation_pages=679-684; citation_doi=10.1512/iumj.1957.6.56038; citation_id=CR47 citation_journal_title=Bull Am Math Soc; citation_title=The theory of dynamic programming; citation_author=R Bellman; citation_volume=60; citation_publication_date=1954; citation_pages=503-515; citation_doi=10.1090/S0002-9904-1954-09848-8; citation_id=CR48 Haarnoja T, Zhou A, Abbeel P, Levine S (2018) Soft actor-critic: off policy maximum entropy deep reinforcement learning with a stochastic actor. In: Proceedings of international conference on machine learning, pp 1861-1870 citation_journal_title=Ann Math Stat; citation_title=A stochastic approximation method; citation_author=H Robbins, S Monro; citation_volume=22; citation_issue=3; citation_publication_date=1951; citation_pages=400-407; citation_doi=10.1214/aoms/1177729586; citation_id=CR50 citation_journal_title=Ann Math Stat; citation_title=Stochastic estimation of the maximum of a regression function; citation_author=J Kiefer, J Wolfowitz; citation_volume=23; citation_issue=3; citation_publication_date=1952; citation_pages=462-466; citation_doi=10.1214/aoms/1177729392; citation_id=CR51 Kingma D, Ba J (2015) Adam: a method for stochastic optimization. In: Proceedings of international conference on learning representations, pp. 1–15 citation_journal_title=Phys Rev; citation_title=On the theory of the brownian motion; citation_author=GE Uhlenbeck, LS Ornstein; citation_volume=36; citation_issue=5; citation_publication_date=1930; citation_pages=823-841; citation_doi=10.1103/PhysRev.36.823; citation_id=CR53 Maas A, Hannun A, Ng A (2013) Rectifier nonlinearities improve neural network acoustic models. In: proceedings of international conference on machine learning, vol 30(1), pp 3 Nair V, Hinton G E (2010) Rectified linear units improve restricted boltzmann machines. In: Proceedings of international conference on machine learning, pp. 807–814 Aich S, Stavness I (2019) Global sum pooling: a generalization trick for object counting with small datasets of large images. In: Proceedings of the IEEE conference on computer vision and pattern recognition workshops, pp. 73–82 citation_journal_title=J Mach Learn Res; citation_title=DEAP: evolutionary algorithms made easy; citation_author=FA Fortin, FM Rainville, MA Gardner, M Parizeau, C Gagné; citation_volume=13; citation_issue=1; citation_publication_date=2012; citation_pages=2171-2175; citation_doi=10.5555/2503308.2503311; citation_id=CR57 citation_journal_title=Swarm Intell; citation_title=Particle swarm optimization: an overview; citation_author=R Poli, J Kennedy, T Blackwell; citation_volume=1; citation_publication_date=2007; citation_pages=33-57; citation_doi=10.1007/s11721-007-0002-0; citation_id=CR58 citation_journal_title=Nat Methods; citation_title=SciPy 1.0: fundamental algorithms for scientific computing in Python; citation_author=P Virtanen, R Gommers, TE Oliphant, M Haberland, T Reddy, D Cournapeau, E Burovski, P Peterson, W Weckesser, J Bright, SJ van der Walt, M Brett, J Wilson, KJ Millman, N Mayorov, ARJ Nelson, E Jones, R Kern, E Larson, CJ Carey, İ Polat, Y Feng, EW Moore, J VanderPlas, D Laxalde, J Perktold, R Cimrman, I Henriksen, EA Quintero, CR Harris, AM Archibald, AH Ribeiro, F Pedregosa, P van Mulbregt, A Vijaykumar, AP Bardelli, A Rothberg, A Hilboll, A Kloeckner, A Scopatz, A Lee, A Rokem, CN Woods, C Fulton, C Masson, C Häggström, C Fitzgerald, DA Nicholson, DR Hagen, DV Pasechnik, E Olivetti, E Martin, E Wieser, F Silva, F Lenders, F Wilhelm, G Young, GA Price, GL Ingold, GE Allen, GR Lee, H Audren, I Probst, JP Dietrich, J Silterra, JT Webber, J Slavič, J Nothman, J Buchner, J Kulick, JL Schönberger, JV de Miranda Cardoso, J Reimer, J Harrington, JLC Rodríguez, J Nunez-Iglesias, J Kuczynski, K Tritz, M Thoma, M Newville, M Kümmerer, M Bolingbroke, M Tartre, M Pak, NJ Smith, N Nowaczyk, N Shebanov, O Pavlyk, PA Brodtkorb, P Lee, RT McGibbon, R Feldbauer, S Lewis, S Tygier, S Sievert, S Vigna, S Peterson, S More, T Pudlik, T Oshima, TJ Pingel, TP Robitaille, T Spura, TR Jones, T Cera, T Leslie, T Zito, T Krauss, U Upadhyay, YO Halchenko, Y Vázquez-Baeza; citation_volume=17; citation_publication_date=2020; citation_pages=261-272; citation_doi=10.1038/s41592-019-0686-2; citation_id=CR59