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Abstract In meshfree methods, the discretized particles or nodes are inter-related by the supports of meshfree shape functions, and thus the support sizes of meshfree shape functions have a significant impact on the meshfree solution accuracy. However, due to the complexity of meshfree shape functions, currently there is still no general guidelines for meshfree support selection, and in practice the meshfree support size is often picked up by trial and error and a uniform support size is set for all particles which cannot ensure the meshfree solution accuracy. In this work, a machine learning approach, namely, the convolutional neural network (CNN), is introduced to optimize the meshfree support selection. It is shown that there is a strong similarity and linkage between the CNN receptive fields and meshfree supports, and accordingly a meshfree intrinsic CNN framework is proposed for meshfree analysis, where the network architecture and the corresponding determination of hyperparameters, such as the convolution kernel size, receptive field size, and their relationships with the number of meshfree nodes, the monomial basis function order and the support size, are particularly detailed for meshfree methods. Subsequently, within the proposed meshfree intrinsic CNN framework, several networks are designed to facilitate the meshfree support selection and solution prediction, in which a single objective like meshfree support selection, or multi-objectives like both meshfree support selection and solution prediction can be realized. Numerical results systematically demonstrate that the proposed meshfree intrinsic CNN framework is very effective to optimize the meshfree support selection with improved solution accuracy.
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Received: 03 November 2020
Published: 17 June 2021
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Corresponding Authors:
王 东东
E-mail: ddwang@xmu.edu.cn
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2021, Vol. 42 
