Abstract We present a deep learning method to investigate the effect of flexoelectricity in nanostructures. For this purpose, deep neural network (DNN) algorithm is employed to map the relation between the inputs and the material response of interest. The DNN model is trained and tested making use of database that has been established by solving the governing equations of flexoelectricity using a NURBS-based IGA formulation at design points in the full probability space of the input parameters. Firstly, pure flexoelectric cantilever nanobeam is investigated under mechanical and electrical loading conditions. Then, structures of composite system constituted by two non-piezoelectric material phases are addressed in order to find the optimized topology with respect to the energy conversion factor. The results show promising capabilities of the proposed method, in terms of accuracy and computational efficiency. The deep learning method we used have produced superior optimal designs compared to the numerical methods. The findings of this study will be of profound interest to researcher involved further in the optimization and design of flexoelectric structures.

中文翻译：

---

一种基于深度学习的新型拓扑优化柔性电纳米结构计算材料设计方法

摘要 我们提出了一种深度学习方法来研究柔性电在纳米结构中的影响。为此，采用深度神经网络 (DNN) 算法来映射输入与感兴趣的材料响应之间的关系。使用基于 NURBS 的 IGA 公式在输入参数的全概率空间中的设计点求解挠曲电控制方程而建立的数据库，对 DNN 模型进行训练和测试。首先，在机械和电负载条件下研究了纯柔性电悬臂纳米梁。然后，解决由两个非压电材料相构成的复合系统的结构，以找到关于能量转换因子的优化拓扑。结果显示了所提出的方法在准确性和计算效率方面的有希望的能力。与数值方法相比，我们使用的深度学习方法产生了卓越的优化设计。这项研究的结果将对进一步参与柔性电结构优化和设计的研究人员产生浓厚的兴趣。