Inversion of Sophisticated Thermal Conductivity via Deep Learning

Identifying the thermophysical properties of unknown material is of great significance in computational heat transfer. In this paper, a deep learning (DL) framework is proposed to reconstruct the temperature or position-dependent thermal conductivity in the 2D region. The framework consists of a denoising network and an inversion network, aiming at inhibiting the noise and reconstruct the thermal conductivity, respectively. The architecture of the denoising network is mainly based on the convolutional neural network (CNN) while the inversion network on the fully connected neural network (FCNN). In order to gain sufficient training data, a forward solver based on the finite element method (FEM), combined with a random thermal conductivity generator, is utilized to compute the boundary temperature. To simulate the actual scenarios, Gaussian noises are added to the calculation results. During the training process, the temperature with noise serves as the input of the denoising network while the generated thermal conductivity is regarded as the target of the inversion network. After 500 epochs of training on Keras, the network eventually achieves convergence. To quantitatively depict the performance of the framework, we define the average relative error rate. As a result, the final error rate is 1.03% for the temperature-dependent situation and 2.65% for the position-dependent one. A great merit for DL techniques is that a well-trained framework can give a forecast almost simultaneously with the given input information. In our network, it only spends 1.732ms to predict the unknown thermal conductivity preciously. Since real-time thermal inversion is more and more widely used in industry, it is anticipated that the proposed framework can be extensively adopted in a variety of scenarios.