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For the temperature field reconstruction (TFR), a complex image-to-imageregression problem, the convolutional neural network (CNN) is a powerfulsurrogate model due to the convolutional layer's good image feature extractionability. However, a lot of labeled data is needed to train CNN, and the commonCNN can not quantify the aleatoric uncertainty caused by data noise. In actualengineering, the noiseless and labeled training data is hardly obtained for theTFR. To solve these two problems, this paper proposes a deep Monte Carloquantile regression (Deep MC-QR) method for reconstructing the temperaturefield and quantifying aleatoric uncertainty caused by data noise. On the onehand, the Deep MC-QR method uses physical knowledge to guide the training ofCNN. Thereby, the Deep MC-QR method can reconstruct an accurate TFR surrogatemodel without any labeled training data. On the other hand, the Deep MC-QRmethod constructs a quantile level image for each input in each training epoch.Then, the trained CNN model can quantify aleatoric uncertainty by quantilelevel image sampling during the prediction stage. Finally, the effectiveness ofthe proposed Deep MC-QR method is validated by many experiments, and theinfluence of data noise on TFR is analyzed.

Deep Monte Carlo Quantile Regression for Quantifying Aleatoric Uncertainty in Physics-informed Temperature Field Reconstruction