6-13. Predicting thermal conductivity of composite materials by deep learning methods

Han Wei, Qingyuan Rong, Shuaishuai Zhao, Hua Bo*

Michigan college, Shanghai jiao tong university

Abstract: Composite materials have wide engineering applications, e.g., automobile industries and aeronautical applications like components of rockets, aircrafts, etc. The effective thermal conductivity is one of the most significant thermo-physical characteristics of the composite material.Accurate prediction of the effective thermal conductivity is critical to the applications and optimal design. However, the structure of composite materials is usually complex, and it is often difficult to establish the linkage between structure and thermal conductivity. In previous studies, the effective medium models have been used to predict the effective thermal conductivity of composites. These models are generally based on a simplified structure and therefore the accuracy is limited. Numerical simulation of thermal diffusion equation or the Boltzmann transport equation can more accurately predict the effective thermal conductivity, but the required computational cost is usually large. In the previous work, we used three machine learning methods to predict the effective thermal conductivity of two-dimensional (2D) composites. Especially, the convolutional neural network (CNN) method achieved the highest accuracy. This method is based on the learning of structural images, where the features of images can be extracted, and the correlation between the images and thermal conductivities can be obtained. The images of the generated composite structures are taken as input and CNN model is learned to obtain the relationship between the composite structure and thermal conductivity. The learned model can accurately predict the new structures.

In reality, most materials often possess 3D structures. Although the prediction accuracy of 3D CNN trained based on 3D microstructures of composites can be high, in real applications, it can be difficult to obtain the detailed 3D microstructures. In comparison, it is very common to extract 2D microscopic images of composites from experiments. Therefore, in this work, we have studied the prediction of the thermal conductivity of 3D composites using CNN with 2D cross section structural images.

First, we generated 3D composites with different structural features using two generation algorithms, QSGS and LS packing. Thermal conductivities of these structures were then calculated using the finite element method as the accurate values. We used two different methods to predict thermal conductivities and compared the predicted thermal conductivities to the accurate thermal conductivities to evaluate the prediction accuracy. First, we used a 3D CNN to learn the characteristics of 3D structures and established a prediction model. The results showed that this model possess high accuracy and low computational cost for predicting the thermal conductivity of new structures. Second, we used representative 2D cross-sectional images of 3D structures to train a 2D CCN model. Compared to the first method, this method is more suitable in the real situation. Because in experiments, it is easier to obtain the cross section of the structure rather than the entire 3D structure. In order to further improve the prediction accuracy, we stacked the cross-sectional images in different directions into multi-channel images to capture the information of structural anisotropy. Strategies such as batch normalization and dropout are also used to avoid over-fitting. We found that larger images contain more information and are therefore more representative, and the corresponding training model has a higher prediction accuracy. At the same time, increasing the number of training images can also improve the prediction accuracy. The results show that the prediction error of the 2D CNN is as low as 3%, which is close to the 3D CNN and far beyond the effective medium theory. Our work further reveals the enormous potential of deep learning methods in predicting material properties and designing optimized material structures.

Keywords: Effective thermal conductivity; Composite material; Deep learning

基于深度学习的复合材料热导率预测

魏晗，容清员，赵帅帅，鲍华*

上海交通大学 密西根学院

摘要：复合材料在自动驾驶，航空航天，能源转换等领域应用广泛。热导率是复合材料最重要的物性参数之一。准确预测复合材料的热导率，对于其应用和优化设计而言至关重要。然而，复合材料的结构一般比较复杂，建立结构和热导率之间的联系往往并不容易。在之前的研究中，人们一般利用等效介质理论模型来快速预测复合材料的等效热导率。这些模型一般基于简化的结构，因此精确度较低。数值求解热扩散方程或者玻尔兹曼输运方程可以更加准确的预测复合材料的等效热导率，但是往往数值计算的成本较高，用时较长。在之前的工作中，我们利用三种机器学习方法准确地预测了二维复合材料的等效热导率。其中，卷积神经网络预测的准确率最高。这种方法基于对图像的学习，可以抽取出图像的特征，并且建立图像和属性之间的关联。我们将生成的复合材料结构的图像作为输入，通过训练卷积神经网络，得到了复合材料结构和热导率之间的联系。学习到的模型可以准确的预测新的结构。实际材料往往是三维结构，虽然基于三维结构的卷积神经网络可以准确的预测热导率，但是获得三维结构在实际的实验中并不容易，而二维的截面是比较容易获得的。所以在这篇文章中我们详细研究了用卷积神经网络基于二维的截面来预测三维复合材料的热导率。

图1.两种不同复合材料的预测误差

首先，我们使用两种生成算法QSGS 和 LS packing生成了具有不同结构特征的三维复合材料。然后利用有限元的方法计算了这些结构的热导率，作为这些材料的“真实”热导率。我们采用了两种不同的方法预测热导率，并比较了预测的热导率与“真实”热导率以获得预测误差。第一种，我们使用三维卷积神经网络学习三维结构的特征并建立其与等效热导率的联系。结果表明，这个模型对于新结构热导率的预测具有很高精度和较低的计算成本。第二种，我们使用三维复合材料的代表性横截面图像（二维）来训练二维卷积神经网络。相比于第一种方法，这种方法更适用于真实情况。因为在实验中，较容易获得的是结构的横切面而不是整个三维结构。为了进一步提高预测精度，我们将不同方向上截面图像连接成多通道图像来捕获结构各向异性的信息。同时也采用了batch normalization和dropout等策略来避免训练过拟合。我们发现，更大尺寸的图像包含更多的信息因此更具代表性，训练模型的预测准确率更高。同时，增加训练的图像数量也能够提高预测准确率。结果表明，二维卷积神经网络的预测误差低至3％，接近三维卷积神经网络，且远优于等效介质理论。我们的工作进一步揭示了深度学习方法在预测材料属性以及设计优化材料结构等方向的巨大应用潜力。

关键词： 热导率；复合材料；深度学习