Effective thermal conductivity estimation using a convolutional neural network and its application in topology optimization

Topology optimization of heterogeneous structures can find significant use in a wide range of applications, and its fabrication has been made possible by recent advances in additive manufacturing. However, the optimization procedure is computationally expensive, as each structural update requires the re-evaluation of the properties. The computational time is the major limiting factor in large-scale and complex structural optimization. In this study, a convolutional neural network (CNN) model for predicting effective thermal conductivity inspired by the VGG networks is proposed. Trained using 130,000 unique binary images, the model achieves high predictive accuracy. Specifically, it shows a mean absolute percent error (MAPE) of 0.35% in testing when the thermal conductivity of the solid is ten times larger than the fluid, and when the thermal conductivities assigned are that of aluminum and water, the MAPE is 2.35%. The prediction time is 15 ms for a single image with 128 x 128 pixels, which is 3 to 5 orders of magnitude faster than a finite volume simulation. When employed in topology optimization, the CNN retains a MAPE between 0.67% and 11.8% for different cases. The CNN model correctly predicts trends in effective thermal conductivity and improves the structure to close proximity of a theoretical maximum in all cases.