Mô hình đại diện dựa trên CNN của phân tích isogeometric trong các vấn đề flexoelectric phi địa phương

Abdel-Hamid O, Mohamed A, Jiang H, Deng L, Penn G, Yu D (2014) Convolutional neural networks for speech recognition. IEEE/ACM Trans Audio Speech Lang Process 22(10):1533–1545 Abdollahi A, Arias I (2015) Constructive and destructive interplay between piezoelectricity and flexoelectricity in flexural sensors and actuators. J Appl Mech 82(12):121003 Abdollahi A, Peco C, Millan D, Arroyo M, Arias I (2014) Computational evaluation of the flexoelectric effect in dielectric solids. J Appl Phys 116(9):093502 Al Rahhal MM, Bazi Y, AlHichri H, Alajlan N, Melgani F, Yager RR (2016) Deep learning approach for active classification of electrocardiogram signals. Inf Sci 345:340–354 Anitescu C, Atroshchenko E, Alajlan N, Rabczuk T (2019) Artificial neural network methods for the solution of second order boundary value problems. Comput Mater Contin 59(1):345–359 Awad M, Khanna R (2015) Support vector regression. In: Pepper J, Weiss S, Hauke P (Eds) Efficient learning machines. Springer, Berlin, pp 67–80 Benner P, Gugercin S, Willcox K (2015) A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Rev 57(4):483–531 Bhaskar UK, Banerjee N, Abdollahi A, Wang Z, Schlom DG, Rijnders G, Catalan G (2016) A flexoelectric microelectromechanical system on silicon. Nat Nanotechnol 11(3):263–266 Buhmann MD (2003) Radial basis functions: theory and implementations, vol 12. Cambridge University Press, Cambridge Cai Y, Zhuang X, Augarde C (2010) A new partition of unity finite element free from the linear dependence problem and possessing the delta property. Comput Methods Appl Mech Eng 199(17–20):1036–1043 Cressie N (1990) The origins of kriging. Math Geol 22(3):239–252 Cross LE (2006) Flexoelectric effects: charge separation in insulating solids subjected to elastic strain gradients. J Mater Sci 41(1):53–63 Duda RO, Hart PE, Stork DG et al (2001) Pattern classification, vol 680. Wiley, New York Ghasemi H, Park HS, Rabczuk T (2017) A level-set based IGA formulation for topology optimization of flexoelectric materials. Comput Methods Appl Mech Eng 313:239–258 Ghasemi H, Park HS, Rabczuk T (2018) A multi-material level set-based topology optimization of flexoelectric composites. Comput Methods Appl Mech Eng 332:47–62 Glorot X, Bordes A, Bengio Y (2011) Deep sparse rectifier neural networks. In: Proceedings of the fourteenth international conference on artificial intelligence and statistics, vol 15, pp 315–323 Gómez A, Vila-Fungueiriño JM, Moalla R, Saint-Girons G, Gázquez J, Varela M, Bachelet R, Gich M, Rivadulla F, Carretero-Genevrier A (2017) Electric and mechanical switching of ferroelectric and resistive states in semiconducting batio3-\(\delta\) films on silicon. Small 13(39):1701614 Goswami S, Anitescu C, Chakraborty S, Rabczuk T (2020) Transfer learning enhanced physics informed neural network for phase-field modeling of fracture. Theor Appl Fract Mech 106:102447 Hamdia KM, Ghasemi H, Bazi Y, AlHichri H, Alajlan N, Rabczuk T (2019) A novel deep learning based method for the computational material design of flexoelectric nanostructures with topology optimization. Finite Elem Anal Des 165:21–30 He K, Gkioxari G, Dollár P, Girshick R (2017) Mask R-CNN. In: Proceedings of the IEEE international conference on computer vision, vol 2017, pp 2961–2969 Hughes TJ, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194(39–41):4135–4195 Jasim A, Wang H, Yesner G, Safari A, Maher A (2017) Optimized design of layered bridge transducer for piezoelectric energy harvesting from roadway. Energy 141:1133–1145 Jia X, Willard J, Karpatne A, Read JS, Zwart JA, Steinbach M, Kumar V (2021) Physics-guided machine learning for scientific discovery: an application in simulating lake temperature profiles. ACM/IMS Trans Data Sci 2(3):1–26 Kim HJ, Seo YD, Youn SK (2009) Isogeometric analysis for trimmed cad surfaces. Comput Methods Appl Mech Eng 198(37–40):2982–2995 Kim Y (2014) Convolutional neural networks for sentence classification. In: EMNLP 2014 - 2014 Conference on Empirical Methods in Natural Language Processing, Proceedings of the Conference, pp 1746–1751. https://doi.org/10.3115/v1/d14-1181 Kögl M, Silva EC (2005) Topology optimization of smart structures: design of piezoelectric plate and shell actuators. Smart Mater Struct 14(2):387 Krichen S, Sharma P (2016) Flexoelectricity: a perspective on an unusual electromechanical coupling. J Appl Mech 83(3):030801 Kwon SR, Huang W, Zhang S, Yuan FG, Jiang X (2016) Study on a flexoelectric microphone using barium strontium titanate. J Micromech Microeng 26(4):045001 LeCun Y, Bottou L, Bengio Y, Haffner P (1998) Gradient-based learning applied to document recognition. Proc IEEE 86(11):2278–2324 Lu H, Liu S, Ye Z, Yasui S, Funakubo H, Rappe AM, Gruverman A (2017) Asymmetry in mechanical polarization switching. Appl Phys Lett 110(22):222903 Merupo VI, Guiffard B, Seveno R, Tabellout M, Kassiba A (2017) Flexoelectric response in soft polyurethane films and their use for large curvature sensing. J Appl Phys 122(14):144101 Mo C, Davidson J, Clark WW (2014) Energy harvesting with piezoelectric circular membrane under pressure loading. Smart Mater Struct 23(4):045005 Myers RH, Montgomery DC, Anderson-Cook CM (2016) Response surface methodology: process and product optimization using designed experiments. Wiley, New York Nanthakumar S, Lahmer T, Zhuang X, Park HS, Rabczuk T (2016) Topology optimization of piezoelectric nanostructures. J Mech Phys Solids 94:316–335 Nanthakumar S, Lahmer T, Zhuang X, Zi G, Rabczuk T (2016) Detection of material interfaces using a regularized level set method in piezoelectric structures. Inverse Probl Sci Eng 24(1):153–176 Nanthakumar S, Zhuang X, Park HS, Rabczuk T (2017) Topology optimization of flexoelectric structures. J Mech Phys Solids 105:217–234 Nguyen-Thanh N, Zhou K, Zhuang X, Areias P, Nguyen-Xuan H, Bazilevs Y, Rabczuk T (2017) Isogeometric analysis of large-deformation thin shells using RHT-splines for multiple-patch coupling. Comput Methods Appl Mech Eng 316:1157–1178 Nowack P, Braesicke P, Haigh J, Abraham NL, Pyle J, Voulgarakis A (2018) Using machine learning to build temperature-based ozone parameterizations for climate sensitivity simulations. Environ Res Lett 13(10):104016 Oliver MA, Webster R (1990) Kriging: a method of interpolation for geographical information systems. Int J Geogr Inf Syst 4(3):313–332 Rabczuk T, Belytschko T (2004) Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int J Numer Methods Eng 61(13):2316–2343 Redmon J, Divvala S, Girshick R, Farhadi A (2016) You only look once: unified, real-time object detection. In: Proceedings of the IEEE conference on computer vision and pattern recognition, vol 2016, pp 779–788 Rupp CJ, Evgrafov A, Maute K, Dunn ML (2009) Design of piezoelectric energy harvesting systems: a topology optimization approach based on multilayer plates and shells. J Intell Mater Syst Struct 20(16):1923–1939 Sainath TN, Mohamed Ar, Kingsbury B, Ramabhadran B (2013) Deep convolutional neural networks for LVCSR. In: 2013 IEEE international conference on acoustics, speech and signal processing, IEEE, pp 8614–8618 Sevilla R, Fernández-Méndez S, Huerta A (2008) NURBS-enhanced finite element method (NEFEM). Int J Numer Methods Eng 76(1):56–83 Shu L, Liang R, Rao Z, Fei L, Ke S, Wang Y (2019) Flexoelectric materials and their related applications: a focused review. J Adv Ceram 8(2):153–173 Smola AJ, Schölkopf B (2004) A tutorial on support vector regression. Stat Comput 14(3):199–222 Srivastava N, Hinton G, Krizhevsky A, Sutskever I, Salakhutdinov R (2014) Dropout: a simple way to prevent neural networks from overfitting. J Mach Learn Res 15(1):1929–1958 Tesche C, De Cecco CN, Baumann S, Renker M, McLaurin TW, Duguay TM, Bayer RR 2nd, Steinberg DH, Grant KL, Canstein C et al (2018) Coronary CT angiography-derived fractional flow reserve: machine learning algorithm versus computational fluid dynamics modeling. Radiology 288(1):64–72 Timoshenko SP, Goodier JN, Abramson HN (1970) Theory of elasticity (3rd ed). J Appl Mech 37(3):888. https://doi.org/10.1115/1.3408648. https://asmedigitalcollection.asme.org/appliedmechanics/article-pdf/37/3/888/5450582/888_1.pdf Tompson J, Goroshin R, Jain A, LeCun Y, Bregler C (2015) Efficient object localization using convolutional networks. In: Proceedings of the IEEE conference on computer vision and pattern recognition, vol 2015, pp 648–656 Wang S, Wang MY (2006) Radial basis functions and level set method for structural topology optimization. Int J Numer Methods Eng 65(12):2060–2090 Yegnanarayana B (2009) Artificial neural networks. PHI Learning Pvt. Ltd., Delhi Yudin P, Tagantsev A (2013) Fundamentals of flexoelectricity in solids. Nanotechnology 24(43):432001 Zhang X, Zhao J, LeCun Y (2015) Character-level convolutional networks for text classification. In: Advances in neural information processing systems, vol 2015, pp 649–657 Zhang X, Pan Q, Tian D, Zhou W, Chen P, Zhang H, Chu B (2018) Large flexoelectriclike response from the spontaneously polarized surfaces in ferroelectric ceramics. Phys Rev Lett 121(5):057602 Zhu Y, Zabaras N, Koutsourelakis PS, Perdikaris P (2019) Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data. J Comput Phys 394:56–81