# Heat Conduction Plate Layout Optimization Using Physics-Driven Convolutional Neural Networks
## 2 Related Work
utilized data-driven Bayesian methods to conduct optimization for generating object shapes with improved drag coefficients [33]. [PERSON] et al. [34] proposed an efficient framework based on generative adversarial network (GAN) for aerodynamic geometric shape optimization. [PERSON] et al. trained a neural network model to infer the flow field and then utilized it as a surrogate model to perform airfoil shape optimization problems based on the gradient descent method. It has been proved that the optimization framework based on DNN could solve general aerodynamic design problems [35]. [PERSON] et al. developed a conditional generative adversarial neural network model to build the mapping between the input parameters and the surface temperature distribution. The author used the sparrow search algorithm to adjust and search the optimal parameters of components [36]. The work described above shows the ability of the deep learning model to predict accurate physical solutions according to precise conditions and presents great potential in optimization tasks. However, these methods are data-driven and also require expensive training sample acquisition costs (numerical simulations or experimental results), which cannot truly address the need to reduce the computational burden [37]. There is also a physics-driven method requiring no or few training data. [PERSON] et al. introduced the laws of physics into machine learning algorithms and named it the physics-informed neural network (PINN) [38]. Introducing the partial differential equations (PDEs) into the loss function, the neural network is trained to meet the corresponding PDEs and boundary conditions and eventually can predict a solution that satisfies physics. Compared with the data-driven methods, it eliminates the dependence of machine learning on training data and significantly reduces the cost of data set generation [39; 40]. In addition, [PERSON] et al. firstly proposed a combined method in which both data and physics guide CNNs to predict the solution of the temperature field [41]. Unlike the conventional data-driven methods of machine learning, a large amount of input data is not essential for physics-driven processes, which significantly improves the practical applicability and feasibility when the data are difficult to obtain [42; 43]. In order to address the optimization issue of heat transfer layout, this work first builds a surrogate model of temperature field computation under the constraint of heat source layout and then specifies the approximation modeling problem of temperature field prediction. Then, to overcome the problem of difficulties in collecting effective layout samples, an optimization strategy is presented, and a data set with superior random distribution characteristics is produced using numerical simulation. Second, a set of benchmark surrogate models for temperature field prediction is built using standard deep neural networks. Finally, the finite element approach is utilized to assess the outcomes of the neural network prediction, and a comprehensive set of surrogate model construction benchmarks based on deep neural networks is established to quantify the prediction accuracy of the surrogate model for the temperature field. When compared to traditional discrete approaches, machine learning has shown promising properties for predicting physics fields [7]. the data-driven technique has been used due to its comparatively long development time utilized in various real physics field inferences. However, in some challenging instances, although a significant number of training samples are used, data-driven approaches have limitations, including difficulty in obtaining solutions that correctly reflect the fundamental physical laws. Using the work in Ref. [28] as an example, even though the number of training samples is 12k, errors persist in the inferred shapes of the flow structure behind the airfoil, and the outputs cannot fully reproduce the real fluid field due to a lack of new information that the model extracts from the existing training data set.