Computational machine learning representation for the flexoelectricity effect in truncated pyramid structures

Khader M. Hamdia, Hamid Ghasemi, Xiaoying Zhuang, Naif Alajlan, Timon Rabczuk

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


In this study, machine learning representation is introduced to evaluate the flexoelectricity effect in truncated pyramid nanostructure under compression. A NonUniform Rational B-spline (NURBS) based IGA formulation is employed to model the flexoelectricity. We investigate 2D system with an isotropic linear elastic material under plane strain conditions discretized by 45×30 grid of B-spline elements. Six input parameters are selected to construct a deep neural network (DNN) model. They are the Young's modulus, two dielectric permittivity constants, the longitudinal and transversal flexoelectric coefficients and the order of the shape function. The outputs of interest are the strain in the stress direction and the electric potential due flexoelectricity. The dataset are generated from the forward analysis of the flexoelectric model. 80% of the dataset is used for training purpose while the remaining is used for validation by checking the mean squared error. In addition to the input and output layers, the developed DNN model is composed of four hidden layers. The results showed high predictions capabilities of the proposed method with much lower computational time in comparison to the numerical model.

Original languageEnglish
Pages (from-to)79-87
Number of pages9
JournalComputers, Materials and Continua
Issue number1
Publication statusPublished - 2019


  • Deep neural networks
  • Flexoelectricity
  • Isogeometric analysis
  • Machine learning prediction

ASJC Scopus subject areas

  • Biomaterials
  • Modelling and Simulation
  • Mechanics of Materials
  • Computer Science Applications
  • Electrical and Electronic Engineering


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