TY - JOUR

T1 - A CNN-based surrogate model of isogeometric analysis in nonlocal flexoelectric problems

AU - Wang, Qimin

AU - Zhuang, Xiaoying

N1 - Funding Information: X. Zhuang and Q. Wang appreciate the funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy within the Cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453) and the ERC Starting Grant COTOFLEXI (Grant no. 802205).

PY - 2023/2

Y1 - 2023/2

N2 - We proposed a convolutional neural network (CNN)-based surrogate model to predict the nonlocal response for flexoelectric structures with complex topologies. The input, i.e. the binary images, for the CNN is obtained by converting geometries into pixels, while the output comes from simulations of an isogeometric (IGA) flexoelectric model, which in turn exploits the higher-order continuity of the underlying non-uniform rational B-splines (NURBS) basis functions to fast computing of flexoelectric parameters, e.g., electric gradient, mechanical displacement, strain, and strain gradient. To generate the dataset of porous flexoelectric cantilevers, we developed a NURBS trimming technique based on the IGA model. As for CNN construction, the key factors were optimized based on the IGA dataset, including activation functions, dropout layers, and optimizers. Then the cross-validation was conducted to test the CNN’s generalization ability. Last but not least, the potential of the CNN performance has been explored under different model output sizes and the corresponding possible optimal model layout is proposed. The results can be instructive for studies on deep learning of other nonlocal mech-physical simulations.

AB - We proposed a convolutional neural network (CNN)-based surrogate model to predict the nonlocal response for flexoelectric structures with complex topologies. The input, i.e. the binary images, for the CNN is obtained by converting geometries into pixels, while the output comes from simulations of an isogeometric (IGA) flexoelectric model, which in turn exploits the higher-order continuity of the underlying non-uniform rational B-splines (NURBS) basis functions to fast computing of flexoelectric parameters, e.g., electric gradient, mechanical displacement, strain, and strain gradient. To generate the dataset of porous flexoelectric cantilevers, we developed a NURBS trimming technique based on the IGA model. As for CNN construction, the key factors were optimized based on the IGA dataset, including activation functions, dropout layers, and optimizers. Then the cross-validation was conducted to test the CNN’s generalization ability. Last but not least, the potential of the CNN performance has been explored under different model output sizes and the corresponding possible optimal model layout is proposed. The results can be instructive for studies on deep learning of other nonlocal mech-physical simulations.

KW - Convolutional neural network

KW - Isogeometric analysis

KW - Nonlocal flexoelectricity

KW - NURBS trimming technique

UR - http://www.scopus.com/inward/record.url?scp=85137018764&partnerID=8YFLogxK

U2 - 10.1007/s00366-022-01717-3

DO - 10.1007/s00366-022-01717-3

M3 - Article

AN - SCOPUS:85137018764

VL - 39

SP - 943

EP - 958

JO - Engineering with Computers

JF - Engineering with Computers

SN - 0177-0667

IS - 1

ER -