Development of an Equation-Free Surrogate Model using Deep Learning Algorithm for Heat Transfer Simulation

The significant computational costs and time associated with accurate simulation of physical phenomena make the simulation of nonlinear systems based on differential equations impractical for real-time prediction. Deep learning with its high potential in understanding nonlinear and unknown phenomena can be a suitable alternative to equation-based modeling. However, the success of deep learning highly relies on the availability of large-scale labeled data. To solve this problem, weakly supervised learning helps us. This algorithm can train models using only a limited amount of labeled data. In this work, a new definition of the loss function was presented, which can greatly reduce our need to prepare labels for network training through weak supervision. We used this approach for 2D heat transfer modeling. The present work consists of two steps: (1) Extracting the equilibrium temperature pattern directly from only 400 thermal data and encoding it in a convolutional kernel that forms the loss function; and (2) unsupervised training of the model using this loss function instead of the labels without observing any thermal data. The effectiveness of the proposed model in terms of accuracy, the number of labeled data used, and the time required for training the network was evaluated and compared with three supervised models trained on large data sets. Despite using less data, our model achieved higher accuracy compared to a supervised model trained from direct observation of 5000 labeled thermal data (0.68% vs. 1.5% error), which has a longer training time than our model (20 vs. 12 hours); and the cGAN-based model despite using more than 10 times more labeled thermal data (0.68% vs. 1% error).