Deep learning-driven topology optimization for heat dissipation of integrated electrical components using dual temperature gradient learning and MMC method

Abstract

Highly integrated electrical components produce intensive heat while in use, which will seriously impact their performance if not properly designed. In this study, an end-to-end heat dissipation structure topology optimization prediction framework considering physical mechanisms was established by using the convolutional neural network (CNN) and the moving morphable components (MMC) method. Aiming at the sparsity of physical field matrix caused by the initial component distribution in MMC method, a CNN model was established taking the temperature gradient information of both homogeneous material and initial component layout as input. Compared with other seven input forms, the CNN model in this study considers both the initial component layout and the physical field information of the structure, which can predict the topology configuration of heat dissipation structure more accurately. In addition, an improved penalty mean square error (PMSE) function was proposed by introducing a penalty factor, which improved the prediction ability of the CNN model on the structural boundary and ensured more accurate and efficient structural heat dissipation performance. Several 2D and 3D numerical examples verified the effectiveness of the proposed framework and the dual temperature gradient input model. The overall framework provides a new method for the innovative and efficient heat dissipation structure topology optimization in packaging structure of electronic equipment.

Appendices

Appendix 1

The hyperparameter related to network training include the number of training rounds (Epoch), batch size, learning rate, etc. This section discusses the selection of hyperparameter related to neural network training according to the CNN structure and loss function form established in the previous content.

Firstly, fix the initial learning rate and discuss different batch sizes. If the Batch size value is too large, it will affect the generalization capability of the model, while if the value is too small, it will lead to gradient oscillation in adjacent iterations, which is not conducive to the convergence of the model. In this section, set the batch size to 4, 8, 16, 32, 64, and train the models to obtain loss function curves under different batch sizes (Fig. 

Fig. 19

The changes in the training loss function value of the model under different Batch size

19). Among them, when Batch size = 4 (blue curve) and Batch size = 8 (red curve), the curve oscillates violently when Epoch is 0–200. To guarantee that the model has strong generalization capability, the loss function value of the model needs to decline steadily. Therefore, Batch size = 4 and Batch size = 8 are not applicable to the current model. At the same time, compared with the Batch size curves of the other three values, it can be seen that when Batch size = 16, the loss function value is small and converges more smoothly. Therefore, 16 is selected here as the Batch size value for the current model training.

Secondly, the setting of the learning rate is directly related to the convergence rate and prediction accuracy of the CNN model. Therefore, this section discusses the value of learning rate. Set the Batch size to 16 and then discuss the various initial learning rates separately. In this section, the learning rate is set to 1e-5, 5e-5, 1e-4, 5e-4, 8e-4. The model is then trained to obtain the loss function curve under different learning rates, as shown in Fig. 

Fig. 20

The changes in the training loss function value of the model under different learning rate”

20.

It is evident from the figure that when the learning rate is 1e-5 (blue curve), the loss function oscillates violently when the Epoch is in the range of 0–200, and drops slowly. When the learning rate is 5e-5 (red curve), the value of the model loss function drops rapidly, and there is no severe oscillation. When the value of the learning rate is further increased, although the loss function value drops rapidly, there is an upward trend in the curve during the convergence stage, indicating that overfitting has occurred currently. Therefore, the learning rate value of 5e-5 is chosen here for the current model training.

For the discussion of hyperparameter Epoch, the Fig. 19 and the Fig. 20 show that the loss function value has not changed significantly after 500 steps of Epoch, and the change of its number will not affect the prediction effect of the model. Therefore, this chapter does not discuss hyperparameter Epoch. Through the above discussion, the hyperparameter settings of the current model are shown in Table

Table 10 The hyperparameter values in the training process of the CNN model

10.

Appendix 2

Figure 

Fig. 21

The schematic diagram of the 3D CNN architecture

21 shows the 3D CNN architecture, and Table

Table 11 The hyperparameters of the proposed 3D CNN architecture

11 shows the hyperparameters of the proposed 3D CNN architecture.

Figures 

Fig. 22

The loss function curve of the 2D CNN model

22 and

Fig. 23

The loss function curve of the 3D CNN model

23 show the convergence process of training the HC-TG model in 2D and 3D cases, respectively. These two figures demonstrate that the training loss and verification loss are in good agreement, without overfitting and under fitting.