A RECURRENT CONVOLUTIONAL NEURAL NETWORK SURROGATE MODEL FOR DYNAMIC MESHFREE ANALYSIS
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摘要: 在无网格动力分析中, 除了无网格形函数本身构造复杂引入的计算成本, 还需要逐步递推求解每个时间步的动力响应, 因而计算效率较为低下. 本文通过研究无网格离散数据与机器学习训练样本、无网格动力分析递推计算过程与循环卷积神经网络序列信息传递模式之间的本征联系, 构建了与无网格法相匹配的循环卷积神经网络设计方法, 进而提出了一种无网格动力分析的循环卷积神经网络代理模型. 该模型充分融合了无网格离散模型节点布置灵活的优点, 同时无网格法能够提供具有泛化特征的高精度数值样本, 增强循环卷积神经网络的泛化性和适用性. 此外, 循环卷积神经网络代理模型特有的循环模块历史记忆特性使其可以有效地处理序列信息, 在保证精度的前提下加速无网格动力分析计算过程. 文中通过系列算例验证了所提出的无网格动力分析的循环卷积神经网络代理模型的精度和效率.Abstract: In addition to the complexity of meshfree approximation that needs extra computational effort, the dynamic meshfree analysis requires the computation of dynamic response recursively at each time step, which significantly lowers the overall computational efficiency. In this work, the intrinsic relationships are established between meshfree discrete data and machine learning training samples, and recursive computational procedure of dynamic meshfree analysis and temporal sequence information transmission mode of recurrent convolution neural networks. With the aid of these intrinsic links, a recurrent convolutional neural network structure design method for meshfree discretization is proposed, which is then used to develop a recurrent convolution neural network surrogate model for dynamic meshfree analysis. This surrogate model takes full advantage of the flexibility of meshfree discretization. Meanwhile, meshfree analysis can provide versatile and highly accurate numerical samples, which then enhance the generality and applicability of the proposed surrogate model for dynamic meshfree analysis. Besides, the unique historical memory characteristics of the recurrent module embedded in the recurrent convolution neural network surrogate model enable an effective processing of the sequence information, and then accelerate the dynamic meshfree computational procedure with accuracy guarantee. The efficiency and accuracy of the recurrent convolution neural network surrogate model for dynamic meshfree analysis are validated through representative examples.
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图 1 全卷积神经网络中的卷积与转置卷积操作
Figure 1. Convolution and transpose convolution operations in full convolution neural networks
图 3 数值计算产生数据与机器学习训练样本之间的对应关系
Figure 3. Schemetic illustration of the corresponding relationship between the data generated by numerical simulations and the machine learning training samples
图 4 无网格动力分析与长短期记忆神经网络之间的本征联系
Figure 4. Intrinsic relationships between dynamic meshfree analysis and long short-term memory neural network
图 5 无网格动力分析的循环卷积神经网络代理模型框架
Figure 5. The structure of recurrent convolution neural network surrogate model for dynamic meshfree analysis
图 6 无网格动力分析训练集包含的计算模型与离散模型
Figure 6. Computational models and discretizations for the training set of dynamic meshfree analysis
图 7 无网格动力分析的循环卷积神经网络代理模型具体数据传递过程
Figure 7. Detailed data transfer process of the recurrent convolution neural network surrogate model for dynamic meshfree analysis
图 8 无网格动力分析的循环卷积神经网络代理模型训练历史
Figure 8. Training history of the recurrent convolution neural network surrogate model for dynamic meshfree analysis
9 方形区域弹性力学问题代理模型预测解与无网格数值解对比
9. Comparison between the predicted solution of the recurrent convolution neural network surrogate model and the meshless numerical solution of the elasticity problem in the square region
图 9 方形区域弹性力学问题代理模型预测解与无网格数值解对比(续)
Figure 9. Comparison between the predicted solution of the recurrent convolution neural network surrogate model and the meshless numerical solution of the elasticity problem in the square region (continued)
图 10 L形区域弹性力学问题代理模型预测解与无网格数值解对比
Figure 10. Comparison between the predicted solution of the recurrent convolution neural network surrogate model and the meshless numerical solution of the elasticity problem in the L-shape region
图 11 圆形区域弹性力学问题代理模型预测解与无网格数值解对比
Figure 11. Comparison between the predicted solution of the recurrent convolution neural network surrogate model and the meshless numerical solution of the elasticity problem in the circular region
图 12 四分之一环形区域弹性力学问题代理模型预测解与无网格数值解对比
Figure 12. Comparison between the predicted solution of the recurrent convolution neural network surrogate model and the meshless numerical solution of the elasticity problem in the quarter annular region
表 1 弹性问题下无网格法动力分析与循环卷积神经网络代理模型训练预测时间对比
Table 1. Comparison of the training and prediction cost between dynamic meshfree analysis and recurrent convolution neural network surrogate model for elastic problems
Items Meshfree simulation/min Meshfree surrogate model/min off-line generation of 9600 sets data — 7520.25 off-line training — 605.30 on-line simulation of 400 sets data 313.34 0.25 
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