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

TL;DR

This paper introduces Deep MC-QR, a novel method that leverages physical knowledge and quantile regression within CNNs to reconstruct temperature fields and quantify aleatoric uncertainty without requiring labeled data.

Contribution

The paper proposes a deep Monte Carlo quantile regression approach that combines physical knowledge with CNNs to perform temperature field reconstruction and uncertainty quantification without labeled data.

Findings

Accurately reconstructs temperature fields in noisy conditions.

Effectively quantifies aleatoric uncertainty caused by data noise.

Validated through extensive experiments demonstrating robustness.

Abstract

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