New loss functions to improve deep learning estimation of heat transfer

Deep neural networks (DNNs) are promising alternatives to simulate physical problems. These networks are capable of eliminating the requirement of numerical iterations. The DNNs could learn the governing physics of engineering problems through a learning process. The structure of deep networks and parameters of the training process are two basic factors that influence the simulation accuracy of DNNs. The loss function is the main part of the training process that determines the goal of training. During the training process, lost function regularly is used to adapt parameters of the deep network. The subject of using DNNs to learn the physical images is a novel topic and demands novel loss functions to capture the physical meanings. Thus, for the first time, the present study aims to develop new loss functions to enhance the training process of DNNs. Here, three novel loss functions were introduced and examined to estimate the temperature distributions in thermal conduction problems. The images of temperature distribution obtained in the present research were systematically compared with the literature data. The results showed that one of the introduced loss functions could significantly outperformance the literature loss functions available in the literature. Using a new loss function improved the mean error by 67.1%. Moreover, using new loss functions eliminated the pixels predictions (with large errors) by 96%.