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Recently, surrogate models based on deep learning have attracted muchattention for engineering analysis and optimization. As the construction ofdata pairs in most engineering problems is time-consuming, data acquisition isbecoming the predictive capability bottleneck of most deep surrogate models,which also exists in surrogate for thermal analysis and design. To address thisissue, this paper develops a physics-informed convolutional neural network(CNN) for the thermal simulation surrogate. The network can learn a mappingfrom heat source layout to the steady-state temperature field without labeleddata, which equals solving an entire family of partial difference equations(PDEs). To realize the physics-guided training without labeled data, we employthe heat conduction equation and finite difference method to construct the lossfunction. Since the solution is sensitive to boundary conditions, we properlyimpose hard constraints by padding in the Dirichlet and Neumann boundaryconditions. In addition, the neural network architecture is well-designed toimprove the prediction precision of the problem at hand, and pixel-level onlinehard example mining is introduced to overcome the imbalance of optimizationdifficulty in the computation domain. The experiments demonstrate that theproposed method can provide comparable predictions with numerical method anddata-driven deep learning models. We also conduct various ablation studies toinvestigate the effectiveness of the network component and training methodsproposed in this paper.

Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Data